Search

This paper presents results on the solvability of the observer design problem for general nonlinear triangular systems with inputs, under weak observability assumptions. The local state estimation is exhibited by means of a delayed time-varying Luenberger-type system. In order to achieve the global estimation, a switching sequence of observers is designed. [ABSTRACT FROM AUTHOR]

In applications, such as biomedicine and systems/synthetic biology, technical limitations in actuation complicate implementation of time-varying control signals. In order to alleviate some of these limitations, it may be desirable to derive simple control policies, such as step functions with fixed magnitude and length (or temporal pulses). In this technical note, we further develop a recently proposed pulse-based solution to the convergence problem, i.e., minimizing the convergence time to the target exponentially stable equilibrium, for monotone systems. In particular, we extend this solution to monotone systems with parametric uncertainty. Our solutions also provide worst case estimates on convergence times. Furthermore, we indicate how our tools can be used for a class of nonmonotone systems, and more importantly how these tools can be extended to other control problems. We illustrate our approach on switching under parametric uncertainty and regulation around a saddle point problems in a genetic toggle switch system. [ABSTRACT FROM PUBLISHER]

While the vast majority of work on consensus and synchronization considers only collaborative interactions among the agents, antagonistic interactions may play important roles in coordination of social systems. In this work, we define a composite model over a stochastically-switching network capturing both collaborative and antagonistic interactions. We consider a general class of agents, so-called conspecifics, defined in terms of a common distribution for their interaction capacity and the weights they ascribe to interactions. We find closed form expressions for necessary and sufficient conditions for consensus, the rate of convergence to consensus, and conditions for stochastic synchronization. This model is further extended to composite topologies capable of capturing any number of independent interaction modes. Results demonstrate the presence of antagonistic interactions may help the system to achieve consensus and synchronization which is not possible in presence of only collaborative interactions and, at times, enables convergence at a faster rate. [ABSTRACT FROM AUTHOR]

The authors develop a dissipativity theory for switched systems whose dynamical modes are described by systems of higher order linear differential equations. They give necessary and sufficient conditions for dissipativity based on systems of linear matrix inequalities (LMIs), constructed from the coefficient matrices of the differential equations describing the modes. The relationship between dissipativity and stability is also discussed, and an application to the stabilization of power converters is provided. [ABSTRACT FROM AUTHOR]

In this paper, we introduce continuous-time linear compartmental switched systems and investigate their stability and stabilizability properties. By their nature, these systems are always stable. Necessary and sufficient conditions for asymptotic stability for arbitrary switching functions, and sufficient conditions for asymptotic stability under certain dwell-time conditions on the switching functions are proposed. Finally, stabilizability is thoroughly investigated and proved to be equivalent to the existence of a Hurwitz convex combination of the subsystem matrices, a condition that, for positive switched systems, is only sufficient for stabilizability. [ABSTRACT FROM AUTHOR]

In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing a class of time-scheduled homogeneous polynomial Lyapunov functions with a sufficiently large degree. The key feature of this nonconservative condition lies in its convexity in the system matrices, which explicitly facilitates its further extension to uncertain systems. Then, in order to obtain numerically testable condition, a family of LMI conditions are presented with the aid of the idea of dividing the dwell-time interval into a finite number of segments. It is proved that the non-conservativeness can be maintained with a sufficiently large interval dividing parameter. In the end, the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices. Numerical examples are presented to illustrate our findings. [ABSTRACT FROM PUBLISHER]

A moment-matching method for model reduction of linear switched systems (LSSs) is presented. The method can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant (LTI) systems. The procedure is based on the so called “nice selections,” which represent a choice of basis in the reachability or observability space of the LSS. The framework can also be used for exact matching of the input-output behavior of an LSS with a reduced order LSS for a specific switching sequence. Conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples. [ABSTRACT FROM PUBLISHER]

This technical note studies switching stabilization problems for continuous-time switched linear systems. We consider four types of switching stabilizability defined under different assumptions on the switching control input. The most general switching stabilizability is defined as the existence of a measurable switching signal under which the resulting time-varying system is asymptotically stable. Discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length. In addition, we define feedback stabilizability in Filippov sense (respectively, sample-and-hold sense) as the existence of a feedback law under which closed-loop Filippov solution (respectively, sample-and-hold solution) is asymptotically stable. It is proved that the four switching stabilizability notions are equivalent and their sufficient and necessary condition is the existence of a piecewise quadratic control-Lyapunov function that can be expressed as the pointwise minimum of a finite number of quadratic functions. [ABSTRACT FROM PUBLISHER]

This note is intended to investigate noise-to-state stability for random nonlinear systems with state-dependent switching. Under some mild and easily verified conditions, the existence of global solution to random switched systems can be proved. Based on a reasonable requirement for the random disturbance, the criteria on noise-to-state stability of random switched systems are presented by the aid of single Lyapunov function technique. The reasonability of the obtained results is illustrated by using a mechanical model in random vibration environment. [ABSTRACT FROM AUTHOR]

Recently a special hybrid system called Switching Markov Jump Linear System (SMJLS) is studied. A SMJLS is subject to a deterministic switching and a stochastic Markovain switching. To extend the results already obtained and to investigate some new aspects of such systems, our main contributions in this paper are: i) Transient analysis of Markov process, i.e., the expectations of the sojourn time, the activation number of any mode, and the number of switchings between any two modes and ii) two sufficient conditions of the exponential almost sure stability for a general SMJLS. Different from previous work, which is a special case of our study, the transition rate matrix for the random Markov process in our study is not fixed, but varies when a deterministic switching takes place. [ABSTRACT FROM AUTHOR]

This note presents a model for switched asynchronous sequential machines (ASMs) and utilizes corrective control to solve their model matching problem. A switched ASM comprising a number of single ASMs or submachines can change its mode or the submachine in which it is operating in an asynchronous mechanism. We obtain a matrix expression for the reachability of switched ASMs, based on which we present the existence condition and design algorithm for a corrective controller that matches the stable-state behavior of the closed-loop system to that of a reference model. The corrective controller for switched ASMs provides not only control input characters but also switching signals to utilize the reachability of each submachine in generating required feedback paths. The constraint on the switching operation caused by the asynchronous mechanism is also discussed. [ABSTRACT FROM PUBLISHER]

This technical note focuses on a class of switched nonlinear systems with unstable modes and switching uncertainties. Both prescribed switching instants and switching sequence of the nominal switching signal would change. Two novel indexes named time changing ratios and mode changing ratios are proposed, based on which several conditions that fully utilize the trade-off among stable and unstable modes are established to achieve the robust stability of the switched system. An example of multi-agent systems illustrates the efficiency of the new results. [ABSTRACT FROM PUBLISHER]

A sufficient condition for the stability of arbitrary switching linear systems (SLSs) without control inputs is that the individual subsystems are stable and their evolution matrices are simultaneously triangularizable (ST). This sufficient condition for stability is known to be extremely restrictive and not robust, and therefore of very limited applicability. The situation can be radically different when control inputs are present. Indeed, previous results have established that, depending on the number of states, inputs and subsystems, the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices are stable and ST can become a generic property, i.e., a property valid for almost every set of system parameters. This note provides novel contributions along two lines. First, we give sufficient conditions for the genericity of the property of existence of feedback matrices so that the subsystem closed-loop matrices are ST (not necessarily stable). Second, we give conditions for the genericity of the property of existence of feedback matrices that, in addition to achieving ST, enable arbitrary eigenvalue selection for each subsystem's closed-loop matrix. The latter conditions are less stringent than existing ones, and the approach employed in their derivation can be interpreted as an extension to SLSs of specific aspects of the notion of eigenvalue controllability for (non-switching) linear systems. [ABSTRACT FROM AUTHOR]

We consider the problem of global stabilization of an unstable bioreactor model (e.g., for anaerobic digestion), when the measurements are discrete and in finite number (“quantized”), with control of the dilution rate. The measurements define regions in the state space, and they can be perfect or uncertain (i.e., without or with overlaps). We show that, under appropriate assumptions, a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion. If the assumptions are not fulfilled, sliding modes may appear, and the transition graphs are not deterministic. [ABSTRACT FROM AUTHOR]

The goal of this technical note is to design a switching signal estimator for a class of elementary continuous-time switching or switched systems. First, the elementary system is recast into a polynomial form and, secondly, some tools borrowed from Algebraic Geometry are used to express the switching signal as a function of the time derivatives of the output and of the input. [ABSTRACT FROM AUTHOR]

In this note, the fault detection filtering problem is solved for nonlinear switched stochastic system in the T-S fuzzy framework. Our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with Brownian motion. Based on observer-based fault detection fuzzy filter as a residual generator, the proposed fault detection is formulated as a fuzzy filtering problem. By the utilization of the average dwell time technique and the piecewise Lyapunov function technique, the fuzzy-parameter-dependent fault detection filters are designed that guarantee the resulted error system to be mean-square exponential stable with a weighted \mathcal H\infty error performance. Then, the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique. Finally, simulation has been presented to show the effectiveness of the proposed fault detection technique. [ABSTRACT FROM AUTHOR]

This paper proposes a Lyapunov-based switching logic within the framework of adaptive mixing control (AMC), where a weighted combination of a family of candidate controllers can be inserted in the loop to regulate the output of an uncertain plant. The proposed AMC scheme employs a bank of parallel estimators, or multiple estimators, together with a switching logic that orchestrates which estimate should be evaluated by the mixer. The switching logic is driven by input/output data and uses Lyapunov-based criteria to assess the best estimate among the bank of parallel estimates. The resulting scheme guarantees convergence of the switching signal in finite time to a controller that satisfies a Lyapunov inequality implying a prescribed stability margin. The problem of convergence to the desired controller is addressed both analytically and numerically. In contrast, most classes of continuous tuning adaptive control or switching adaptive control schemes do not guarantee that after the switching stops or the adaptation is switched off the resulting closed loop linear time-invariant (LTI) system is stable, unless there is sufficient plant excitation that guarantees convergence to the desired fixed parameter controller. The proposed scheme guarantees that if the desired controller is switched on, it will never be switched off thereafter. Furthermore, simulations demonstrate that while alternative adaptation methods can converge to an LTI unstable feedback loop, the proposed scheme consistently converges to the desired controller. [ABSTRACT FROM AUTHOR]

In this paper we deal with the stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity. [ABSTRACT FROM AUTHOR]

We consider discrete-time linear time-invariant (LTI) systems with state feedback, where the actuation signal is subject to switching propagation delays, due to, e.g., routing in a multi-hop communication network. We show how to model these systems as pure switching linear systems and provide an algorithm for robust stability analysis. Next, we turn to the design problem and provide an algorithm that computes in a finite number of steps the look-ahead knowledge of the delays (i.e., routing) necessary to achieve controllability and stabilizability. This generalizes well known controllability criteria for LTI systems. [ABSTRACT FROM AUTHOR]

Leader-follower formation control is a widely used distributed control strategy that requires systems to exchange their information over a wireless radio communication network to attain and maintain formations. These wireless networks are often subject to deep fades, where a severe drop in the quality of the communication link occurs. Such deep fades inevitably inject a great deal of stochastic uncertainties into the system, which significantly impact the system's performance and stability, and cause unexpected safety problems in applications like smart transportation systems. Assuming an exponentially bursty channel that varies as a function of the vehicular states, this paper proposes a distributed switching control scheme under which the local controller is reconfigured in response to the changes of channel state, to assure almost sure safety for a chain of leader-follower system. Here almost sure safety means that the likelihood of vehicular states entering a safe region asymptotically goes to one as time goes to infinity. Sufficient conditions are provided for each local vehicle to decide which controller is placed in the feedback loop to assure almost sure safety in the presence of deep fades. Simulation results of a chain of leader-follower formation are used to illustrate the findings. [ABSTRACT FROM PUBLISHER]

This technical note deals with the design of mode-dependent H\infty filters for a class of discrete-time switched systems with nonlinearities. In this class of systems, when the system mode changes, the filter designed for the specific subsystem also switches accordingly. The main contribution is on the use of the information of the sojourn probability—the probability of the switched system staying in each subsystem—to build new kind of switched system model when this additional information is available. Sojourn probabilities are easier to obtain than the transition probabilities commonly used in Markovian jump systems. Applying the Lyapunov functional method, the bounded real lemma (BRL) for the resulting filtering error system is obtained in Theorem 1. The filter parameters are designed in Theorem 2 by solving a set of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the effectiveness and potential of the proposed approach. [ABSTRACT FROM AUTHOR]

In this technical note, we solve the control problem of rigid bodies with only quaternion measurements for all initial rotations and angular velocities. The proposed solution is based on the theory of cascades using any switching certainty equivalence controller satisfying certain assumptions along with an in the large hybrid observer. The equilibrium point of the proposed observer in closed loop with the rigid body dynamics is proven to be $\kappa$-exponentially stable in the large i.e., we prove that the equilibrium point is stable and that the error states converge exponentially fast towards the origin for all initial rotations and angular velocities. Until now, stability results for quaternion-based observers have typically only been valid for a bounded set of initial conditions. To overcome this issue, our observer design is based on dynamic scaling and switching logic. Furthermore, we show that the origin of the proposed switching certainty equivalence controller in closed loop with the hybrid observer is asymptotically stable in the large for all available initial conditions associated with the quaternion space. Simulation results for the proposed scheme are presented with the particular case of the PD $+$ controller, revealing that all states converge as expected from our theoretical findings. [ABSTRACT FROM AUTHOR]

We analyze the feedback passivity of a networked control system in which the control packets may be dropped by the communication channel. Specifically, we consider a discrete-time switched nonlinear system with relative degree zero that switches between two modes. At the instants when the communication link transmits the packet successfully, the system evolves in closed-loop and the increase in storage function is bounded below the energy supplied by the control input. At the instants when a packet drop occurs, the system evolves in open loop according to the free dynamics of the closed-loop mode and the increase in storage function is not necessarily bounded by the supplied energy. The literature on passivity of switched systems seems to consider only the case when all the modes are passive, which is not the case here. We prove that if the ratio of time steps for which the system evolves in closed-loop versus in open loop is lower bounded by a critical number, the system is locally feedback passive in a suitably defined sense. This generalized definition of feedback passivity is useful since it preserves two important properties of classical passivity—that feedback passivity implies asymptotic stabilizability for zero state detectable systems and that feedback passivity is preserved in parallel and negative feedback interconnections. [ABSTRACT FROM AUTHOR]

This technical note is concerned about the finite-time stability and stabilization for Itô stochastic systems with Markovian switching. A mode-dependent parameter approach is proposed to give a sufficient condition for finite-time stability, and its superiority to common parameter approach is analyzed. Moreover, the finite-time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities. A N-mode algorithm is given for solving the obtained matrix inequalities arising from finite-time stability(stabilization). Finally, an example is employed to illustrate the effectiveness of our obtained results. [ABSTRACT FROM AUTHOR]

This technical note considers the global finite-time stability problem for a class of switched nonlinear systems with the cyclic switching sequence, dissipative or non-dissipative impulsive effects may appear at each switching instant, and each mode may or may not be finite-time stable individually. A new concept named cycle dwell time is proposed based on which two stability conditions are established. These conditions fully reveal the trade-off among each mode's dynamics, impulsive dynamics and initial conditions. An example of multi-agent systems illustrates the efficiency of the new results. [ABSTRACT FROM PUBLISHER]

The consensus problems with H\infty and weighted H\infty bounds for a homogeneous team of linear time-invariant (LTI) multi-agent systems with a switching topology and directed communication network graph are studied in this technical note. Sufficient conditions to design distributed controllers are proposed based on state feedback corresponding to bounded L2 gain and rms bounded disturbances. Based on the solution of an algebraic Riccati equation that circumvents the need to solve linear matrix inequalities (LMIs), a design methodology is proposed to properly select the controller gains. The stability properties of the proposed controllers are then investigated based on Lyapunov analysis. The effectiveness of our proposed consensus algorithms are then illustrated by performing simulations for diving consensus of a team of unmanned underwater vehicles (UUVs). [ABSTRACT FROM AUTHOR]

Checking validity of a model is a crucial step in the process of system identification. This is especially true when dealing with switched affine systems since, in this case, the problem of system identification from noisy data is known to be generically NP-Hard and can only be solved in practice by using heuristics and relaxations. Therefore, before the identified models can be used for instance for controller design, they should be systematically validated against additional experimental data. In this paper we address the problem of model (in)validation for multi-input multi-output switched affine systems in output error form with unknown switches. As a first step, we prove that necessary and sufficient invalidation certificates can be obtained by solving a sequence of convex optimization problems. In principle, these problems involve increasingly large matrices. However, as we show in the paper by exploiting recent results from semialgebraic geometry, the proposed algorithm is guaranteed to stop after a finite number of steps that can be be explicitly computed from the a priori information. In addition, this algorithm exploits the sparse structure of the underlying optimization problem to substantially reduce the computational burden. The effectiveness of the proposed method is illustrated using both academic examples and a non-trivial problem arising in computer vision: activity monitoring. [ABSTRACT FROM AUTHOR]

This technical note aims to introduce stability analysis of Lur'e-type switched systems in frequency domain. A new state-input dependent switching function is proposed and it is the key issue to obtain a stability condition that generalizes the celebrated Popov criterion to deal with this class of switched nonlinear systems. Likewise the case of time invariant systems, we propose a frequency domain stability test that is expressed through a convex combination of the subsystems state space matrices. This task is not trivial due to the time-varying nature of the nonlinear systems under consideration. The theory is illustrated by a simple example. [ABSTRACT FROM AUTHOR]

Most existing works on adaptive control of discrete-time systems focus on the case of linear parametrization. For nonlinearly parameterized systems, the stabilizability turns out to be an intractable issue. This technical note is devoted to seeking the essential factors that determine the stabilizability of nonlinearly parameterized discrete-time systems. A sufficient condition imposed on the structures of the system functions is established. Analysis shows that the sensitivity function of unknown parameters plays a crucial role in characterizing the uncertainties of parameterized systems. One of the implications of this result is that arbitrarily growing nonlinearities in the uncertain model may be allowed for global stabilization. [ABSTRACT FROM AUTHOR]

This technical note is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part. The stochastic stability of such switched systems is studied using a Lyapunov approach. A necessary and sufficient condition is established in terms of linear matrix inequalities. The effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition. [ABSTRACT FROM PUBLISHER]

This technical note studies the synchronization of coupled discrete-time harmonic oscillators with rational frequency under switching topology. The remarkable feature of this problem is that the conditions that merely involve the connectivity structure of topology does not suffice for synchronizing the oscillators. We propose a frequency dependent topology condition that indicates in what way the topology switches, and introduce firmly nonexpansive mapping (FNM) from functional analysis. Under the condition, the synchronization of coupled oscillators is related to an infinite product of FNMs, which share only one zero common fixed point. By a convergence result on infinite product of a finite number of FNM, we present a synchronization result for the coupled oscillators. Finally, a simulation example is given to illustrate the effectiveness of the result. [ABSTRACT FROM AUTHOR]

In this technical note, a novel methodology for robust finite-time stabilization of a chain of uncertain fractional order integrator is proposed. This is achieved by first designing a nominal controller which stabilizes the system in finite time. An integral sliding-mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding-mode control is the negative of the disturbance and hence the disturbance is cancelled. An improved strategy with more general kind of uncertainty is also proposed. Numerical examples are presented to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of controlling an uncertain time-varying plant by means of a finite family of candidate controllers supervised by an appropriate switching logic. It is assumed that, at every time, the plant consists of an uncertain single-input/single output linear system. It is shown that stability of the switched closed-loop system can be ensured provided that 1) at every time there is at least one candidate controller capable of potentially stabilizing the current time-invariant “frozen” plant model, and 2) the plant changes are infrequent or satisfy a slow drift condition. [ABSTRACT FROM AUTHOR]

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. While minimum-dwell time results require the subsystems to be asymptotically stable, mode-dependent dwell-time results can consider unstable subsystems and dwell-times within a, possibly unbounded, range of values. The proposed approach is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A state-dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed. Sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each subsystem such that it is non-increasing at the switching instants. During the dwell time, this function varies piecewise linearly in time. After the dwell, the system switches if the switching results in a decrease in the value of the LF. The method proposed is also applicable to robust stabilization via state-feedback. It is further extended to guarantee a bound on the \cal L2-gain of the switching system; it is also used in deriving state-feedback control law that robustly achieves a prescribed \cal L2-gain bound. [ABSTRACT FROM AUTHOR]

In this note, we consider switched systems and switched systems with state reset. In particular we focus on the case of partial reset, i.e., where only some state components may undergo the action of a reset. First we consider switched systems with pre-specified (partial) reset and investigate under which conditions such systems are stable. In a second stage we consider the problem of stabilization by (partial) reset, which consists in finding a suitable (partial) reset for a given switched system that makes this system stable under arbitrary switching. [ABSTRACT FROM AUTHOR]

An adaptive approach is proposed to address the problem of robustification (and performance loss reduction) of anti-windup (AW) compensation in the presence of large uncertainties. The approach relies on the augmentation of the AW compensator with an adaptive robustifying filter; a constructive procedure is provided for designing such a filter. The use of adaptation allows to reduce the conservativeness of previous robust approaches to what is needed to preserve stability with respect to the uncertainty actually present on the plant during operation, as detected by input and output plant measurement. [ABSTRACT FROM AUTHOR]

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability. [ABSTRACT FROM AUTHOR]

An epidemic that spreads in a network calls for a decision on the part of the network users. They have to decide whether to protect themselves or not. Their decision depends on the tradeoff between the perceived infection and the protection cost. Aiming to help users reach an informed decision, security advisories provide periodic information about the infection level in the network. We study the best-response dynamic in a network whose users repeatedly activate or de-activate security, depending on what they learn about the infection level. Our main result is the counterintuitive fact that the equilibrium level of infection increases as the users' learning rate increases. The same is true when the users follow smooth best-response dynamics, or any other continuous response function that implies higher probability of protection when learning a higher level of infection. In both cases, we characterize the stability and the domains of attraction of the equilibrium points. Our finding also holds when the epidemic propagation is simulated on human contact traces, both when all users are of the same best-response behavior type and when they are of two distinct behavior types. [ABSTRACT FROM AUTHOR]

The standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty. In the case where the latter polytope is large, the design may become very conservative. We present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem. Assuming that there is online information on which of the regions the parameters of the system move to, a recently developed method for H\infty design of switched system with dwell time is applied. A Lyapunov Function (LF) in a quadratic form, which is non-increasing at the switching instants, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the \cal L2 -gain of the switched system. The obtained results are used to solve the corresponding robust H\infty state-feedback and static output-feedback control problems. [ABSTRACT FROM AUTHOR]

The technical note studies a class of linear systems whose piecewise-constant dynamic matrix is subject to both stochastic jumps, governed by a Markov chain, and deterministic switches. These systems will be dubbed switching dynamics Markov jump linear systems (SD-MJLS). Sufficient conditions for exponential almost sure stability (EAS-stability) are established under either hard or average constraints on the dwell-time between switching instants. The proof relies on easy-to-check norm contractivity conditions and the ergodic law of large numbers. [ABSTRACT FROM AUTHOR]

This paper deals with model reduction by balanced truncation of switched linear systems (SLS). We consider switched linear systems whose dynamics, depending on the switching signal, switches between finitely many linear systems with a common state space. These linear systems are called the modes of the SLS. The idea is to seek for conditions under which there exists a single state space transformation that brings all modes of the SLS in balanced coordinates. As a measure of reachability and observability of the state components of the SLS, we take the average of the diagonal gramians. We then perform balanced truncation by discarding the state components corresponding to the smallest diagonal elements of this average balanced gramian. In order to carry out this program, we derive necessary and sufficient conditions under which a finite collection of linear systems with common state space can be balanced by a single state space transformation. Among other things, we derive sufficient conditions under which global uniform exponential stability of the SLS is preserved under simultaneous balanced truncation. Likewise, we derive conditions for preservation of positive realness or bounded realness of the SLS. Finally, in case that the conditions for simultaneous balancing do not hold, or we simply do not want to check these conditions, we propose to compute a suitable state space transformation on the basis of minimization of an overall cost function associated with the modes of the SLS. We show that in case our conditions do hold, this transformation is in fact simultaneously balancing, bringing us back to the original method described in this paper. [ABSTRACT FROM AUTHOR]

This technical note presents a new method for stability analysis and stabilization of sampled-data systems with control packet loss. It is assumed that if the control packet from the controller to the actuator is lost, then the actuator input to the plant is set to zero. The new method is based on a novel construction of piecewise differentiable Lyapunov functionals by using an impulsive system representation of sampled-data systems. A significant feature of the new Lyapunov functionals is that they are continuous at impulse times but not necessarily positive definite inside the impulse intervals. Applying the new Lyapunov functionals to sampled-data systems with control packet loss, improved criteria for stability and stabilization are derived. The new criteria are proved theoretically to be less conservative than the existing results. Illustrative examples are given which substantiate the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider the problem of designing controllers to steer mobile robots to the source (the minimizer) of a signal field. In addition to the mobility constraints, e.g., posed by the nonholonomic dynamics, we assume that the field is completely unknown to the robot and the robot has no knowledge of its own position. Furthermore, the unknown field is randomly switching. In the case where the information of the field (e.g., the gradient) is completely known, standard motion planning techniques for mobile robots would converge to the known source. In the absence of mobility constraints, convergence to the minimum of unknown fields can be pursued using the framework of numerical optimization. By considering these facts, this paper exploits an idea of the stochastic approximation for solving the problem mentioned in the beginning and proposes a source seeking controller which sequentially generates the next waypoints such that the resulting discrete trajectory converges to the unknown source and which steers the robot along the waypoints, under the assumption that the robot can move to any point in the body fixed coordinate frame. To this end, we develop a rotation-invariant and forward-sided version of the simultaneous-perturbation stochastic approximation algorithm as a method to generate the next waypoints. Based on this algorithm, we design source seeking controllers. Furthermore, it is proven that the robot converges to a small set including the source in a probabilistic sense if the signal field switches periodically and sufficiently fast. The proposed controllers are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

The problem of parametric estimation of harmonic signals in the presence of noise and computational constraints is an important issue in many engineering fields. This technical note proposes an algorithm for frequency and bias estimation under noisy measurements. An approach for high-frequency noise rejection by switching is proposed and applied for improvement of the estimation accuracy. Efficiency of the approach is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

A combined multiple model adaptive control (CMMAC) scheme, which is a proper combination of the estimator-based MMAC scheme and the unfalsified MMAC scheme, has been proposed with the aim of taking advantage of the strength of each scheme while avoiding their weaknesses. The major novelty of the CMMAC scheme lies in the fact that it monitors not only the adequacy of candidate models in terms of their estimation performances but also the performance of the active candidate controller. As an application of the CMMAC scheme and one example of such new multiple model adaptive controllers, a CMMAC based controller has been designed for a class of nonlinear systems with nonlinear parameterization. Under some sufficient conditions, a strong finite time switching result (which provides a characterization on the maximum number of switching) and the closed-loop stability have been established. A constructive design based on back-stepping is provided for the adaptive control problem of a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability. [ABSTRACT FROM PUBLISHER]

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques. [ABSTRACT FROM PUBLISHER]

This paper studies the quadratic regulation problem for discrete-time switched linear systems (DSLQR problem) on an infinite time horizon. A general relaxation framework is developed to simplify the computation of the value iterations. Based on this framework, an efficient algorithm is developed to solve the infinite-horizon DSLQR problem with guaranteed closed-loop stability and suboptimal performance. Due to these guarantees, the proposed algorithm can be used as a general controller synthesis tool for switched linear systems. [ABSTRACT FROM PUBLISHER]

This paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events (switching systems). Parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes. To deal with the hybrid nature of the system, and the possible discontinuities of its solutions at switching times, a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed. The innovative design of the discrete-time dynamics of the compensator guarantees the robust existence of a steady-state response giving zero tracking error in the controlled output, and local convergence to it. [ABSTRACT FROM AUTHOR]