For my latest publications, please consult my Google Scholar page. I hope to update this webpage soon and in the mean time, you will find my publications only up till 2017 here.
The preprints of my articles can be found on
HAL
Please consult the publisher's website for final version and appropriate citations of the results.
You may find the following legend useful:
[J]: Journal [C]: Conference proceedings with peer reviews [Bc]: Book chapter
[W]: Workshop/Meetings without peer review [p]: preprirnt/ unpublished article
2017:
[C19] Stabilization with Event-Driven Controllers over a Digital Communication Channel
A. Tanwani, A. Teel
56th IEEE Conf. on Decision and Control, 2017.
Abstract
Publisher's Link
The paper considers the problem of stabilization of hybrid systems when the transmission of information packets between the plant and controller is affected by random events. Stability results are derived using Lyapunov functions.
[C18] Stabilization of Boundary Controlled Hyperbolic PDEs via Lyapunov-Based Event Triggered Sampling and Quantization
N. Espitia, A. Tanwani, S. Tarbouriech
56th IEEE Conf. on Decision and Control, 2017.
Abstract
Preprint
Publisher's Link
With the growing utility of hyperbolic systems in modeling physical and controlled systems, this paper considers the problem of stabilization of boundary controlled hyperbolic partial differential equations where the output measurements are communicated after being time-sampled and space-quantized. Static and dynamic controllers are designed, which establish stability in different norms with respect to measurement errors using Lyapunov-based techniques. For practical purposes, stability in the presence of event-based sampling and quantization errors is analyzed. The design of sampling algorithms ensures practical stability.
[pJ12] Disturbance-to-State Stabilization and Quantized Control for Linear Hyperbolic Systems
A. Tanwani, C. Prieur, S. Tarbouriech
provisionally accepted in IEEE Trans. Automat. Control in Sep. 2017, but never resubmitted.
Abstract
arXiv Link
We consider a system of linear hyperbolic PDEs where the state at one of the boundary points is controlled using the measurements of another boundary point. Because of the disturbances in the measurement, the problem of designing dynamic controllers is considered so that the closed-loop system is robust with respect to measurement errors. Assuming that the disturbance is a locally essentially bounded measurable function of time, we derive a disturbance-to-state estimate which provides an upper bound on the maximum norm of the state (with respect to the spatial variable) at each time in terms of L-infinity-norm of the disturbance up to that time. The analysis is based on constructing a Lyapunov function for the closed-loop system, which leads to controller synthesis and the conditions on system dynamics required for stability. As an application of this stability notion, the problem of quantized control for hyperbolic PDEs is considered where the measurements sent to the controller are communicated using a quantizer of finite length. The presence of quantizer yields practical stability only, and the ultimate bounds on the norm of the state trajectory are also derived.
[Bc3] Asymptotic stabilization of some finite and infinite dimensional systems by means of dynamic event-triggered output feedbacks
C. Prieur, A. Tanwani.
Chap. 8 in Feedback Stabilization of Controlled Dynamical Systems (In honor of L. Praly), Lecture Notes in Control and Information Sciences, Volume 473, 2017.
Publisher's link
[pJ11] Well-posedness and output regulation for implicit time-varying evolution variational inequalities
A. Tanwani, B. Brogliato, C. Prieur
to appear in SIAM J. Control and Optimization.
Abstract
arXiv Link
A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first study the conditions for existence and uniqueness of solutions. The central idea behind the proof is to rewrite the system dynamics as a differential inclusion which can be decomposed into a single-valued Lipschitz map, and a time-dependent maximal monotone operator. Regularity assumptions on the set-valued mapping determine the regularity of the resulting solutions. Complementarity systems with time-dependence are studied as a particular case. We then use this result to study the problem of designing state feedback control laws for output regulation in systems described by EVIs. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed. As applications, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. Another application is seen in designing control inputs for regulation in power converters.
[J10] Determinability and state-estimation for switched differential-algebraic equations.
A. Tanwani, S. Trenn
Automatica, 76:17-31, 2017.
Abstract
Publisher's Link
The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems
are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying dynamic and static
(in the form of algebraic constraints) relations on the evolution of state trajectories, an appropriate notion of observability
is presented which accommodates these phenomena. Based on this notion, we first derive a formula for the reconstruction of the
state of the system where we explicitly obtain an injective mapping from the output to the state. In practice, such a mapping
may be difficult to realize numerically and hence a class of estimators is proposed which ensures that the state estimate
converges asymptotically to the real state of the system.
[C17] Observer Design for Detectable Switched DAEs.
A. Tanwani, S. Trenn
IFAC World Congress, 2017.
Abstract
Preprint
Publisher's Link
This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application in synthesis of observers. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor over that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component in the estimator is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.
2016:
[J9] Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization
A. Tanwani, C. Prieur, M. Fiacchini.
Systems and Control Letters, 94:46-56, 2016.
Abstract
Preprint
Publisher's link
We consider the problem of output feedback stabilization in linear systems when
the measured outputs and control inputs are subject to event-triggered sampling
and dynamic quantization. A new sampling algorithm is proposed for outputs which
does not lead to accumulation of sampling times and results in asymptotic stabilization
of the system. The approach for sampling is based on defining an event function
that compares the difference between the current output and the most recently
transmitted output sample not only with the current value of the output,
but also takes into account a certain number of previously transmitted
output samples. This allows us to reconstruct the state using an observer with
sample-and-hold measurements. The estimated states are used to generate a
control input, which is subjected to a different event-triggered sampling routine;
hence the sampling times of inputs and outputs are asynchronous.
Using Lyapunov-based approach, we prove the asymptotic stabilization of
the closed-loop system and show that there exists a minimum inter-sampling
time for control inputs and for outputs. To show that these sampling routines
are robust with respect to measurement errors, only the quantized (in space)
values of outputs and inputs are transmitted to the controller and the plant,
respectively. A dynamic quantizer is adopted for this purpose, and an algorithm
is proposed to update the range and the center of the quantizer that results in an
asymptotically stable closed-loop system.
[J8] Observer design for frictionless and unilaterally constrained Lagrangian systems: A passivity-based approach
A. Tanwani, B. Brogliato, C. Prieur.
IEEE Transactions on Automatic Control, 61(9):2386-2401, 2016. DOI: 10.1109/TAC.2015.2492098
Abstract
Preprint
Publisher's link
Animations
This paper addresses the problem of estimating the velocity variables, using the
position measurement as output, in nonlinear Lagrangian dynamical systems with
perfect unilateral constraints.
Using the class of bounded variation functions to model the velocity variables
(so that Zeno phenomenon is not ruled out), we represent the derivative of such
functions with the Lebesgue-Stieltjes measure, and use the framework of measure
differential inclusion (MDI) to describe the dynamics at velocity level which naturally
encodes the relations for prescribing the post-impact velocity.
Under the assumption that the velocity of the system is uniformly bounded,
an observer is designed which is also a measure differential inclusion.
It is proved that there exists a unique solution to the proposed observer and
that solution converges asymptotically to the actual velocity.
[C16] Input-to-state stabilization in H^1-Norm for boundary controlled linear hyperbolic PDEs with application to quantized control
A. Tanwani, C. Prieur, S. Tarbouriech.
IEEE Conf. on Decision and Control, 2016.
Abstract
We consider a system of linear hyperbolic PDEs where the state at one of the boundary points is controlled using the measurements of another boundary point.
For this system class, the problem of designing dynamic controllers for input-to-state stabilization in $\cH^1$-norm with respect to measurement errors is considered.
The analysis is based on constructing a Lyapunov function for the closed-loop system which leads to controller synthesis and the conditions on system dynamics required for stability.
As an application of this stability notion, the problem of quantized control for hyperbolic PDEs is considered where the measurements sent to the controller are communicated using a quantizer of finite length.
The presence of quantizer yields practical stability only, and the ultimate bounds on the norm of the state trajectory are also derived.
[C15] Differential-algebraic inclusions with maximal monotone operators
K. Camlibel, L. Iannelli, A. Tanwani, S. Trenn.
IEEE Conf. on Decision and Control, 2016.
Abstract
The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems.
The existence of solutions is proved using the tools from the theory of maximal monotone operators.
The class of solutions that we study in the paper have the property that, instead of the whole state, only $Px$ is absolutely continuous and unique.
This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations.
Certain class of irregular DAEs are also covered within the proposed general framework.
Applications from electrical circuits are included to provide a practical motivation.
2015:
[J7] Stability notions for a class of nonlinear systems with measure controls
A. Tanwani, B. Brogliato, C. Prieur.
Mathematics of Controls, Signals and Systems, vol. 27(2), pp. 245-275, 2015.
Abstract
Preprint
Publisher's link
We consider the problem of stability in a class of
differential equations which are driven by a differential measure associated with inputs of
locally bounded variation. After discussing some existing notions of solution for such systems,
we derive conditions on the system's vector fields for asymptotic stability under a specific
class of inputs. These conditions are based on the stability margin of the Lebesgue-integrable
and the measure-driven components of the system. In case the system is not asymptotically stable,
we derive weaker conditions such that the norm of the resulting trajectory is bounded by some
function of the total variation of the input, which generalizes the notion of integral
input-to-state stability in measure-driven systems.
[J6] Comments on “Observability of switched linear systems: Characterization and observer design”
A. Tanwani, H. Shim, D. Liberzon.
IEEE Transactions on Automatic Control, vol. 60(12), pp. 3396-3400.
Abstract
Preprint
Publisher's link
This technical note points out certain limitations of our results from the paper mentioned in the title and provides a
modified approach to overcome these limitations. In particular, the observer design addressed in the aforementioned paper
is, in general, only applicable to switched linear systems with invertible state reset maps and this note presents a
modified algorithm for state estimation that can also handle non-invertible state reset maps. In the process, we also
identify some equalities from that paper which may not hold in general for arbitrary state reset maps.
[C14] On using norm-estimators for event-triggered control with dynamic output feedback
A. Tanwani, A. Teel, C. Prieur.
IEEE Conf. on Decision and Control, 2015.
Abstract
For feedback stabilization of a control system using dynamic output feedback, we consider the problem of finding two different sequences of time instants at which the sampled outputs (respectively, control inputs) must be sent to the controller (resp.~the plant). Instead of static inequalities, the states of so-called norm estimators are used to determine sampling instants. Using the tools from Lyapunov theory for hybrid systems and stability of cascaded nonlinear systems, it is shown that the closed loop system is globally asymptotically stable. Additional assumptions are required on the controller and system dynamics to guarantee that the proposed sampling routines do not lead to an accumulation of sampling times over a finite interval.
[C13] On detectability of switched linear differential-algebraic equations
A. Tanwani, S. Trenn.
IEEE Conf. on Decision and Control, 2015.
Abstract
This paper addresses the notion of detectability for continuous-time switched systems comprising linear differential-algebraic equations (DAEs).
It relates to studying asymptotic stability of the set of state trajectories corresponding to zero input and zero output.
Due to the nature of solutions of switched DAEs, the problem reduces to stability of the trajectories emanating from a non-vanishing unobservable subspace, for which we first derive a geometric expression based on our recent work on observability.
The stability of state trajectories starting from a certain subspace can then be check in two possible ways.
In the first case, detectability of switched DAE is shown to be equivalent to the asymptotic stability of a reduced order discrete-time switched system.
In the second approach, the solutions from a non-vanishing unobservable subspace are mapped to the solutions of a continuous reduced order time-varying switching ordinary differential equations (ODEs).
As a special case of the later approach, the reduced order system is time-invariant if the unobservable subspace is invariant.
[W3] Estimation and control problems in Moreau's sweeping process
A. Tanwani at SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah (USA), 2015.
[W2] Output regulation in differential variational inequalities using internal model principle and passivity-based approach.
A. Tanwani at GAMM Annual Workshop, Lecce, Italy, 2015.
Preprint
(to appear in Proceedings in Applied Mathematics and Mechanics, published by Wiley)
[Bc2] Observer Design for Switched Linear Systems with State Jumps
A. Tanwani, H. Shim, D. Liberzon.
Hybrid Dynamical Systems, Lecture Notes in Control and Information Sciences Volume 457, pp. 179-203, 2015.
Publisher's link
[Bc1] Observability of Switched Linear Systems
M. Petreczky, A. Tanwani, S. Trenn.
Hybrid Dynamical Systems, Lecture Notes in Control and Information Sciences Volume 457, pp. 205-240, 2015.
Publisher's link
2014:
[J5] Stability and observer design for multivalued Lur'e systems with non-monotone, time-varying nonlinearities and
state jumps
A. Tanwani, B. Brogliato, C. Prieur.
SIAM J. Control and Optimization, vol. 52(6), pp. 3639-3672, 2014.
Abstract
Preprint
Publisher's link
Simulation Code (needs
SICONOS kernel to generate data)
This paper deals with the stability and observer design for
Lur'e systems with multivalued nonlinearities, which are not necessarily monotone or
time-invariant. Such differential inclusions model the motion of state trajectories which are
constrained to evolve in time-varying non-convex sets. Using Lyapunov-based analysis,
sufficient conditions are proposed for local stability in such systems, while specifying the
basin of attraction. If the sets governing the motion of state trajectories are moving with
bounded variation, then the resulting state trajectories are also of bounded variation, and
unlike the convex case, the stability conditions depend on the size of jumps allowed in the sets.
Based on the stability analysis, a Luenberger-like observer is proposed which is shown to
converge asymptotically to the actual state provided the initial value of the state estimation
error is small enough. In addition, a semi-global practically stable observer, based on the
high-gain approach, is designed to reduce the state estimation error to the desired accuracy
in finite time which is then combined with the locally convergent observer to obtain
semi-global asymptotically convergent state estimates.
[J4] Hybrid-type observer design based on a sufficient condition for
observability in switched nonlinear systems
H. Shim, A. Tanwani.
Int. Jnl. of Robust and Nonlinear Control (Special issue), vol. 24 (6), pp. 1064-1089, April 2014.
Abstract
Preprint
Publisher's link
Matlab Simulation Code (Courtesy: H. Shim)
This paper presents a sufficient condition for observability of continuous-time switched nonlinear systems that also involve state jumps.
Without assuming observability of individual modes, the sufficient condition is based
on gathering partial information from each mode so that the state is completely
recovered after several switchings.
Based on the sufficient condition, a hybrid-type observer is designed, which comprises
a copy of the actual plant and an error correction scheme at discrete time instants.
In order to execute the proposed design, the observable component of the state at
each mode needs to be estimated without transients or peaking (caused by
high-gain observers), and this motivates us to introduce a back-and-forth estimation technique.
Under the assumption of persistent switching, analysis shows that the estimate thus
generated converges asymptotically to the actual state of the system.
Simulation results validate the utility of proposed algorithm.
[C12] On output regulation in systems with differential variational inequalities
A. Tanwani, B. Brogliato, C. Prieur.
accepted in IEEE Conf. Decision and Control (invited session on
variational analysis in systems and control), December 2014.
Abstract
Preprint
We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems
which are described by variational inequalities and ordinary differential equations. In our setup, these variational
inequalities are used to model state trajectories constrained to evolve within time-varying, closed, and convex sets,
and systems with complementarity relations.
We first derive conditions to study the existence and uniqueness of solutions in such systems.
The derivation of control laws for output regulation is based on the use of internal model principle,
and two cases are treated: first, a static feedback control law is derived when full state feedback is available;
In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator
is designed. As applications, we demonstrate how control input resulting from the solution of a variational
inequality results in regulating the output of the system while maintaining polytopic state constraints.
Another application is seen in designing switching signals for regulation in power converters.
[C11] On output regulation in state-constrained dynamical systems:
An application to polyhedral case
A. Tanwani, B. Brogliato, C. Prieur.
IFAC World Congress (invited session on output regulation in hybrid
systems), August 2014.
Abstract
Preprint
This paper deals with the problem of output regulation using the state feedback
control laws for a class of nonsmooth dynamical systems where the state is
constrained to evolve within some convex set. The formalism of differential
inclusions (DIs) is used to describe the system dynamics and the derivation of
the state feedback law is based on the internal model principle. We study two
types of control laws: firstly, a static control is designed assuming that the
entire states of the plant and the exosystem are available for feedback; In the
second case, only the error to be regulated is available for feedback and a
dynamic compensator is designed. The analyses are based on using the properties
of the normal cones associated with convex sets to study the well-posedness
(existence and uniqueness of solutions) and the stability of the closed-loop
system. As an application, we design a discontinuous controller which guarantees
the viability of a predefined polyhedral subset of the state space using the
formulation of linear complementarity systems.
2013:
[J3] Observability of switched linear systems: Characterization and observer design
A. Tanwani, H. Shim, D. Liberzon.
IEEE Transactions on Automatic Control, vol. 58 (4), pp. 891-904, April 2013.
Abstract
PDF (also contains erratum)
Publisher's link
Matlab Simulation Code
This paper presents a characterization of observability and an observer design method for switched linear systems with
state jumps. A necessary and sufficient condition is presented for observability,
globally in time, when the system evolves under predetermined mode transitions.
Because this characterization depends upon the switching signal under consideration,
the existence of singular switching signals is studied alongside developing a
sufficient condition that guarantees uniform observability with respect to switching
times. Furthermore, while taking state jumps into account, a relatively weaker
characterization is given for determinability, the property that concerns with
recovery of the original state at some time rather than at all times. Assuming
determinability of the system, a hybrid observer is designed for the most general
case to estimate the state of the system and it is shown that the estimation error
decays exponentially. Since the individual modes of the switched system may not be
observable, the proposed strategy for designing the observer is based upon a novel idea
of accumulating the information from individual subsystems. Contrary to the usual approach,
dwell-time between switchings is not necessary, but the proposed design does require
persistent switching. For practical purposes, the calculations also take into account
the time consumed in performing computations.
[C10] Passivity-based observer design for a class of Lagrangian systems with
perfect unilateral constraints
A. Tanwani, B. Brogliato, C. Prieur.
Proc. 52nd IEEE Conf. Decision and Control, Florence, Italy, December 2013.
Abstract
Preprint
This paper addresses the problem of estimating the velocity
variables, using the position measurement as output, in nonlinear Lagrangian dynamical systems
with perfect unilateral constraints. The dynamics of such systems are formulated as a measure
differential inclusion (MDI) at velocity level which naturally encodes the relations for
prescribing the post-impact velocity.
Under the assumption that the velocity of the system is uniformly bounded, an observer is
designed which is also a measure differential inclusion. It is proved that there exists a
unique solution to the proposed observer and that solution converges asymptotically to the
actual velocity.
[C9] An observer for switched differential-algebraic equations based on geometric characterization of observability
A. Tanwani, S. Trenn.
Proc. 52nd IEEE Conf. Decision and Control (invited session on control aspects of switched systems), Florence, Italy, December 2013.
Abstract
Preprint
Matlab Simulation Example
Based on our previous work dealing with geometric characterization of observability for switched differential-algebraic equations (switched DAEs),
we propose an observer design for switched DAEs that generates an asymptotically convergent
state estimate. Without assuming the observability of individual modes, the central idea in
constructing the observer is to filter out the maximal information from the output of each of
the active subsystems and combine it with the previously extracted information to obtain a good
estimate of the state after a certain time has passed. In general, observability only holds when
impulses in the output are taken into account, hence our observer incorporates the knowledge of
impulses in the output. This is a distinguished feature of our observers design compared to
observers for switched ordinary differential equations.
[C8] On Stability of measure driven differential equations
A. Tanwani, B. Brogliato, C. Prieur.
9th IFAC Symposium on Nonlinear Control Systems,
Toulouse, France, Sep 2013.
Abstract
Preprint
We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with the inputs of locally bounded variation.
After discussing some existing notions of solution for such systems,
we derive conditions on the system's vector fields for asymptotic stability under a specific class of inputs.
These conditions present a trade-off between the Lebesgue-integrable and the measure-driven components of the system.
In case the system is not asymptotically stable, we derive weaker conditions such that the norm of the resulting trajectory is
bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state
stability in measure-driven systems.
[W1] Observer design for a class of Langrangian systems with impacts.
A. Tanwani
Second workshop on nonsmooth mechanics, Grenoble, France, 2013.
2012:
[C7] Observability of switched differential-algebraic
equations for general switching signals
A. Tanwani, S. Trenn.
Proc. 51st IEEE Conf. Decision and Control, Maui, Hawaii, December 2012.
Abstract
Preprint
We study observability of switched differential algebraic
equations (DAEs) for arbitrary switching. We present
a characterization of observability and, a related property
called, determinability. These characterizations utilize the results
for the single-switch case recently obtained by the authors.
Furthermore, we study observability conditions when only the
mode sequence of the switching signal (and not the switching
times) are known. This leads to necessary and sufficient
conditions for observability and determinability. We illustrate
the results with illustrative examples.
[C6] Back-and-forth operation of state observers and
norm estimation of estimation error
H. Shim, A. Tanwani, Z. Ping.
Proc. 51st IEEE Conf. Decision and Control, Maui, Hawaii, December 2012.
Abstract
Preprint
In contrast to classical observers operating synchronously
with the plant, this paper proposes a state estimation algorithm that executes Luenberger observers in a back-and-forth
manner using the stored inputs and output signals. One
benefit of this technique is the rapid convergence of state
estimation error without relying on high injection gain, so
that the amplification of measurement noise is much relieved.
Moreover, by operating the observer in the proposed manner,
we obtain an upper bound on the estimation error independent
of its initial value. Some real-time applications of the proposed
idea, and the effect of disturbances, are also discussed.
2011:
[J2] An inversion-based approach to fault detection and isolation in switching electrical networks
A. Tanwani, A. D. Dominguez-Garcia, D. Liberzon.
IEEE Trans. on Control Systems Technology, vol. 19 (5), pp. 1059-1074, 2011.
Abstract
PDF
Publisher's link
Matlab Simulation Code (needs PLECS plugin to simulate the boost converter)
This paper proposes a framework for fault detection and isolation (FDI) in electrical energy systems based on techniques
developed in the context of invertibility of switched systems. In the absence of
faults--the nominal mode of operation--the system behavior is described by one set
of linear differential equations or more in the case of systems with natural
switching behavior, e.g., power electronics systems. Faults are categorized as
hard and soft. A hard fault causes abrupt changes in the system structure, which
results in an uncontrolled transition from the nominal mode of operation to a
faulty mode governed by a different set of differential equations. A soft fault
causes a continuous change over time of certain system structure parameters,
which results in unknown additive disturbances to the set(s) of differential
equations governing the system dynamics. In this setup, the dynamic behavior of
an electrical energy system (with possible natural switching) can be described
by a switched state space model where each mode is driven by possibly known and
unknown inputs. The problem of detection and isolation of hard faults is
equivalent to uniquely recovering the switching signal associated with
uncontrolled transition caused by hard faults. The problem of detection and
isolation of soft faults is equivalent to recovering the unknown additive
disturbance caused by the fault. Uniquely recovering both switching signal and
unknown inputs is the concern of the (left) invertibility problem in switched
systems, and we are able to adopt theoretical results on that problem, developed
earlier, to the present FDI setting. The application of the proposed framework
to fault detection and isolation in switching electrical networks is illustrated
with several examples.
[C5] Robust invertibility of switched linear systems
A. Tanwani, D. Liberzon.
Proc. 50th IEEE Conf. Decision and Control, Orlando, FL, December 2011.
Abstract
Preprint
In this paper, we address the effects
of uncertainties in output measurements and initial conditions on invertibility
of the switched systems -- the problem concerned with the recovery of the input
and the switching signal using the output and the initial state. By computing
the reachable sets and maximal error in the propagation of state trajectories
through the inverse system, we derive conditions under which it is possible to
recover the exact switching signal over a certain time interval, provided the
uncertainties are bounded in some sense. In addition, we discuss separately the
case where each subsystem is minimum phase and it is possible to recover the
exact switching signal globally in time. The input, though, is recoverable only
up to a neighborhood of the original input.
[C4] On a sufficient condition for observability of switched nonlinear systems and observer design strategy
H. Shim, A. Tanwani.
Proc. American Control Conf., San Francisco, CA, June 2011.
Abstract
Preprint
This paper presents a sufficient condition
for observability of switched systems that involve state jumps and comprise
nonlinear dynamical subsystems affine in control. Without assuming observability
of individual modes, the sufficient condition is based on gathering partial
information from each mode so that the state is recovered completely after some
time. Using this result, an observer is designed which employs a novel 'back-and-forth'
technique to generate state estimates. Under the assumption of persistent switching,
analysis shows that the estimate converges asymptotically to the actual state
of the system.
[C3] Observability implies observer design for switched linear systems
A. Tanwani, H. Shim, D. Liberzon.
Proc. ACM Conf. Hybrid Systems: Computation and Control, Chicago, IL, Apr 2011.
Abstract
Preprint
Erratum
Matlab Simulation Example
This paper presents a unified framework
for observability and observer design for a class of hybrid systems. A necessary
and sufficient condition is presented for observability, globally in time, when
the system evolves under predetermined mode transitions. A relatively weaker
characterization is given for determinability, the property that concerns with
unique recovery of the state at some time rather than at all times. These
conditions are then utilized in the construction of a dynamic observer that is
feasible for implementation in practice. The observer, without using the
derivatives of the output, generates the state estimate that converges to the
actual state under persistent switching.
2010 and before:
[J1] Invertibility of nonlinear switched systems
A. Tanwani, D. Liberzon.
Automatica, vol. 46 (12), pp. 1962-1973, 2010.
Abstract
PDF
Publisher's link
Matlab Simulation Code (linear case)
This article addresses the invertibility problem for switched nonlinear systems a ne in controls. The
problem is concerned with reconstructing the input and switching signal uniquely
from given output and initial state. We extend the concept of switch-singular
pairs, introduced recently, to nonlinear systems and develop a formula for
checking if the given state and output form a switch-singular pair. A necessary
and sufficient condition for the invertibility of switched nonlinear systems is
given, which requires the invertibility of individual subsystems and the
nonexistence of switch-singular pairs. When all the subsystems are invertible,
we present an algorithm for finding switching signals and inputs that generate a
given output in a finite interval when there is a finite number of such switching
signals and inputs. Detailed examples are included to illustrate these newly
developed concepts.
[C2] On observability of switched differential-algebraic equations
A. Tanwani, S. Trenn.
Proc. 49th IEEE Conf. Decision and Control, Atlanta, GA, December 2010.
Abstract
Full text
We investigate observability of switched differential algebraic equations. The
article primarily focuses on a class of switched systems comprising of two modes
and a switching signal with single switching instant. We provide a necessary and
sufficient condition under which it is possible to recover the value of state
trajectory (globally in time) with the help of switching phenomenon, even though
the constituent subsystems may not be observable. In case the switched system is
not globally observable, we discuss the concept of forward observability which
deals with the recovery of state trajectory after the switching. A necessary and
sufficient condition that characterizes forward observability is presented.
Several examples are included for better illustration of the key concepts.
[C1] Invertibility of nonlinear switched systems
A. Tanwani, D. Liberzon.
Proc. 47th IEEE Conf. Decision and Control, Cancun, Mexico, December 2008.
Abstract
Full text
This article addresses the invertibility problem for switched nonlinear systems
affine in controls. The problem is concerned with finding the input and
switching signal uniquely from given output and initial state. We extend the
concept of switch-singular pairs, to nonlinear systems and develop a formula for checking if given state and
output form a switch-singular pair. We give a necessary and sufficient condition
for a switched system to be invertible, which says that the subsystems should be
invertible and there should be no switch-singular pairs. When all the subsystems
are invertible, we present an algorithm for finding switching signals and inputs
that generate a given output in a finite interval when there is a finite number
of such switching signals and inputs. Detailed examples are included to
illustrate these newly developed concepts.
Phd Thesis
Invertibility and Observability of Switched Systems
with Inputs and Outputs
Adviser: Daniel Liberzon
Committee Members: D. Liberzon (Chair), P. R. Kumar, A. Dominguez-Garcia, S. Mitra
Completed: December, 2011.