Supervisory control using a new control-relevant switching

This paper presents a new supervisory control scheme, which is based on a control-relevant switching logic. Unlike most of the existing switching methods considering only estimator performance, the proposed scheme takes both estimator and controller performance into account. As an index to the controller performance, an iISS (integral-input-to-state stability) Lyapunov function is employed; it is ensured that the Lyapunov function satisfies a certain inequality. This Lyapunov-based switching is then coupled to the state-dependent dwell-time switching developed recently, and the state of the uncertain plant is shown to converge asymptotically. The proposed supervisory control scheme is applied to an input-constrained neurally stable linear plant.     

Modular supervisory control of discrete-event systems

A modular approach to the supervisory control of a class of discrete-event systems is formulated, and illustrated with an example. Discrete-event systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions. The basic problem of interest is to ensure by appropriate supervision that the closed loop behavior of the system lies within a given legal behavior. Assuming this behavior can be decomposed into an intersection of component restrictions, we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion. The work of this author was supported by NSERC (Canada) under Grant No. A-7399. The work of this author was supported by the National Science Foundation through Grant No. ECS-8504584.     

On the control of discrete-event dynamical systems

We study a class of problems related to the supervisory control of a discrete-event system (DES), as formulated by Ramadge and Wonham, and we focus on the computational effort required for their solution. While the problem of supervisory control of a perfectly observed DES may be easily solved by dynamic programming, the problem becomes intractable (in the sense of complexity theory) when imperfectly observed systems are considered. Research supported by the Army Research Office (Grant No. DAAL03-86-K-0171) and by an NSF PYI award, with matching funds from Bellcore Inc.     

Hysteresis-based switching algorithms for supervisory control of uncertain systems

We address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers. We present a new hysteresis-based switching logic, designed specifically for this purpose, and derive a bound on the number of switches produced by this logic on an arbitrary time interval. The resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics.     

Online control of discrete-event systems: A survey

In control theory, as in other areas of engineering research, there is an inherent tension between the breadth of a technique’s applicability and its mathematical tractability. For the area of discrete-event systems (DES), this manifested itself in a theory of supervisory control that originally provided correct-by-construction guarantees for offline solutions to a restricted kind of deterministic process. Follow-on work extended the reach of these techniques to a number of new settings, notably the development of online control without sacrificing any of the original DES performance guarantees. The ability to enact online control opened the door to applying DES techniques to the adaptive control processes presented by modern technologies: processes with dynamic and time-varying natures, whose characteristics may be understood poorly or not at all. Although many works have built on the seminal work of online control in DES, we believe that these ideas have not reached their full potential due to the difficulty in translating them to adjacent fields. In this survey, we look back at 30 years of research concerning the online control of DES and closely related limited lookahead policies with an eye to making the works accessible to practitioners in the broader control theory and artificial intelligence communities. We conclude with some thoughts on future research directions for the further development and application of online DES control techniques to problems requiring intelligent control in our modern world.     

Input-to-state stability of switched systems and switching adaptive control

In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.     

Optimal control of switching systems

This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang-bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.     

Receding horizon control of switching systems

This paper exploits the concept of periodic invariance in order to derive a novel predictive control algorithm for switched systems. The offline computation here concerns the definition of sequences of switches which return the state vector to a set after a given number of moves, while an online optimization is used to improve performance by exploiting information available on the value of the state at each time instant. The algorithm is shown to have closed loop stability and to ensure that the state is steered to a bounded set of ellipsoids centered on the target state. The results of the paper are illustrated by means of a numerical example.     

Supervisory fault tolerant control for a class of uncertain nonlinear systems

This paper focuses on the design of a unique scheme that simultaneously performs fault isolation and fault tolerant control for a class of uncertain nonlinear systems with faults ranging over a finite cover. The proposed framework relies on a supervisory switching among a family of pre-computed candidate controllers without any additional model or filter. The states are ensured to be bounded during the switching delay, which ends when the correct stabilizing controller has been selected. Simulation results about a flexible joint robotic example illustrate the efficiency of the proposed method.     

Synthesis of product-driven coordination controllers for a class of discrete-event manufacturing systems

A synthesis approach is proposed for discrete-event coordination architectures applied to a class of automated manufacturing systems (AMS) in which a clear separation is established between equipment control activities and product manufacturing procedures. Manufacturing procedures are modeled by regular languages constructed with a class of control commands named imperative. Equipment controllers are synthesized as a standard discrete-event supervisors dealing only with operational and safety issues of equipment groupings. The control of equipment modules is carried out following the imperative control commands sequences. Conditions are established to guarantee that the manufacturing procedure of a given product can be achieved using the synthesized supervisors in a particular AMS. Therefore, equipment controllers are not needed to be modified to consider the manufacturing of different products, whilst the construction of achievable manufacturing procedures becomes an “ad hoc” simple process using a reduced set of procedural blocks. The approach is illustrated with an experimental AMS.     

Stability and switching control design issues for a class of discrete time hybrid systems

For the class of systems considered, necessary and sufficient stabilizability conditions are unknown. However, by considering the same systems with unknown but bounded exogenous disturbances, we give finitely computable conditions, sufficient for stabilizability without disturbances, yet necessary for stabilizability with disturbances.     

Supervisory control of hybrid systems within a behavioural framework

This contribution addresses the synthesis of supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. We find an l-complete approximation (abstraction) Σ_l for Σ, represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists, we synthesize the maximally permissive supervisor for Σ_l. We show that it also solves the control problem for the hybrid system Σ. If no solution exists, approximation accuracy can be increased by computing a k-complete abstraction Σ_k, k>l. This paper is entirely set within the framework on Willems’ behavioural systems theory.     

Supervisory control of production-distribution systems with saturation decisions

In this paper, the supervisor implementation which guarantees good performance for saturation operation and prevents reset windup is presented. Moreover, the bounded-input bound-output (BIBO) stability for saturated systems using supervisory control with a dynamic controller is provided in the time domain.     

Decentralized switching control for hierarchical systems

In this paper, a decentralized switching scheme is introduced for uncertain interconnected systems with a structure which is “approximately hierarchical”, and where the switching controller acts on the control agents independently of each other. In this problem, it is assumed that the plant at any point of time can be described by a finite set of linear time-invariant (LTI) finite-dimensional models, but that the switching controller does not require any knowledge of these plant models; the only requirement made is that there exists a known finite set of decentralized controllers, containing at least one controller which can stabilize and regulate the actual physical plant at any time. Simulation results obtained for the proposed decentralized switching controller are given.     

On the controllability of switching linear systems

This note presents a necessary and sufficient condition for small time controllability of a linear switching system (that is, a collection of linear time-invariant control systems, where a trajectory is any concatenation of trajectories of the individual systems). This result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone.     

Lyapunov-based switching control of nonlinear systems using high-gain observers

We consider output feedback stabilization of uniformly observable uncertain nonlinear systems when the uncertain parameters belong to a known but comparably large compact set. In a previous paper, we proposed a new logic-based switching control to improve the performance of continuous high-gain-observer-based sliding mode controllers. Our main goal here is to show that similar techniques can be exploited for solving challenging control problems for a more general class of uncertain nonlinear systems. We require neither the sign of the high-frequency gain to be known nor the system to be minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if, after a dwell-time period, the derivative of the Lyapunov function does not satisfy a certain inequality. A high-gain observer is used to estimate the derivatives of the output as well as the derivative of the Lyapunov function. Another goal of this paper is to introduce a switching strategy that uses on-line information to decide on the controller to switch to, instead of using a pre-sorted list as in our previous work. The new strategy can improve the transient performance of the system.     

Supervisory control with state-dependent dwell-time logic and constraints

The paper deals with the supervisory control of a nonlinear uncertain system in which the switching is directed by the recently introduced state-dependent dwell-time switching logic. The proposed supervisory control architecture is shown to regulate to zero the state of the system without requiring the switching to stop in finite time. A significant class of systems to which the control architecture can be applied is the class of linear systems with input saturation.     

一类切换模糊时滞系统的状态反馈控制

针对切换模糊时滞系统,根据平行分布补偿算法,设计了模糊状态反馈控制器.使用切换技术及单Lyapunov函数和多Lyapunov函数方法,给出了这一类切换模糊时滞系统渐近稳定的充分条件及切换律.仿真结果表明了方法的有效性.     

Overcoming the limitations of adaptive control by means of logic-based switching

In this paper we describe a framework for deterministic adaptive control which involves logic-based switching among a family of candidate controllers. We compare it with more conventional adaptive control techniques that rely on continuous tuning, emphasizing how switching and logic can be used to overcome some of the limitations of traditional adaptive control. The issues are discussed in a tutorial, non-technical manner and illustrated with specific examples.     

On a switching control scheme for nonlinear systems with ill-defined relative degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input–output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tomlin and Sastry (Systems Control Lett. 35(3) (1998) 145) is applicable for a wider class of nonlinear systems.