A reference governor approach for constrained piecewise affine systems

This paper addresses the hybrid control design of discrete-time piecewise-affine systems subject to actuator saturation under event-triggering mechanism. Conditions to ensure regional stability are proposed, and the region of asymptotic stability is determined for piecewise-affine systems by modelling actuator saturation as a piecewise-affine model for each subsystem. Event-triggered feedback control gains can be obtained for single-input piecewise-affine systems by solving a linear matrix inequality issue based on the event-triggering mechanism. In particular, an optimisation method for determining a larger domain of attraction is provided, using ellipsoidal approximations to estimate the domain of attraction. The effectiveness of the proposed results is demonstrated through simulation examples.

This paper presents a novel observer-based controller design method for discrete-time piecewise affine (PWA) systems. The basic idea is as follows: at first, a piecewise linear (without affine terms) state feedback controller and a PWA observer are designed separately, and then it is proved that the output feedback controller constructed by the resulting observer and state feedback controller gains can guarantee the stability of the closed-loop system. During the controller design, the piecewise-quadratic Lyapunov function technique is used. Moreover, the region information is taken into account to treat the affine terms, so the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically feasible with commercially available software. Three simulation examples are given finally to verify the proposed theoretical results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

We consider the problem of controlling a discrete-time piecewise affine (PWA) system from a specification given as a Linear Temporal Logic (LTL) formula over linear predicates in its state variables. We present a computational framework for finding initial states and feedback control strategies guaranteeing the satisfaction of such a specification by all the trajectories of the closed loop system. Our solution is based on abstracting the system to a finite transition system and on controlling the abstraction from an LTL specification.

In a quick motion system, the shortest setting time is usually pursued, while for a system existing both input constraint and state constraints, by using traditional reference governor, maybe there are one phenomenon: some state don't achieve maximal valve due to shape of invariant set, This will lead to a longer setting time. This paper provides a method to shorten setting time of output via an outer feedback based on traditional reference governor. Outer feedback is computed by solving a convex non-constrained quadratic optimization. For linear system with outer feedback, different invariant set is computed based on reference governor. Meanwhile, this paper describes a built process of serval invariant sets and provides a most big invariant set just to fulfill the first receding horizon to get the shortest setting time.

Reference governors enforce pointwise-in-time state and control constraints by temporarily modifying the reference command to a nominal closed-loop system whenever the danger of constraint violation exists. In this paper we propose a reference governor with the added capability of resetting internal closed-loop system states as necessary to avoid constraint violation. With this approach the constrained domain of attraction, i.e., the set of states recoverable without constraint violation, is enlarged. This scheme is referred to as the controller state and reference governor. The paper describes this scheme, analyzes its stability and convergence properties, and presents examples of applying it to aircraft flight control and gas turbine engine control examples.

In the setting of discrete-time linear systems with unmeasured set-bounded disturbances, this paper proposes a control scheme that combines a disturbance free input-constrained Model Predictive Control (uMPC) policy and a reference governor (RG) which modifies the reference command to enforce constraints that are not enforced by the uMPC policy. Such a scheme, referred to as the robust RGMPC, can handle (possibly nonlinear) state and input constraints and only requires solving an optimisation problem for MPC with polytopic input constraints, for which fast algorithms exist. Conditions are given which ensure recursive feasibility of the robust RGMPC scheme, finite-time convergence of the modified reference command to the desired reference command and asymptotic convergence of the state to an invariant neighbourhood of the associated set-point. Simulation results for a constrained spacecraft rendezvous manoeuvre demonstrate that the rRGMPC scheme has lower average computational time than several robust state and input-constrained MPC controllers.

The reference governor is an add-on scheme to a pre-stabilized system that enforces pointwise-in-time state and control constraints. It does so by monitoring and minimally adjusting the reference command to ensure system response to the adjusted reference satisfies prescribed constraints. Conventional approaches to reference governor design rely on explicit models of the system. In this paper, we propose a reference governor approach for systems that admit only implicit models and are subject to set-bounded disturbance inputs. To ensure constraint satisfaction in the presence of uncertain but set-bounded disturbances, the proposed reference governor exploits metric regularity, a tool from variational analysis. We illustrate the effectiveness and online feasibility of the proposed reference governor approach through a power system example.

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This paper proposes a new formulation for the Reference Governor (RG) applied to linear systems affected by exogenous disturbances, specifically those large enough to cause constraint violation. This formulation is based on a set-theoretic approach which includes external disturbances within a new RG, that we call Recovery RG (RRG). The idea is to update the Maximal Output Admissible Set (MAS) and compute a constraint-admissible input that recovers the system from constraint violation at steady-state. The proposed RRG overcomes some of the limitations of standard RG schemes, and maintains their desirable features such as formulation simplicity and finite time determination of the MAS. We validate this new scheme by simulating a linearized turbocharged gasoline engine affected by additive disturbances.

In this paper we consider discrete-time piecewise affine systems with boolean inputs, outputs and states and show that they can be represented in a logic canonical form where the logic variables influence the switching between different submodels but not the continuous-valued dynamics. We exploit this representation for studying Lagrange stability and developing performance analysis procedures based on linear matrix inequalities. Moreover, by using arguments from dissipativity theory for non-linear systems, we generalize our approach to solve the H ∞ analysis problem.

This paper presents robust stabilizability analysis and stabilizing state-feedback controller design for discrete-time piecewise affine systems in the presence of disturbance inputs. The piecewise affine plant leads to an increasing sequence of robust symbolic models by extending existing symbolic models to the case where bounded disturbance inputs, as well as control inputs, affect the state transfer. A numerical example illustrates the developed analysis and design approaches.

This paper dealt with the stabilization problem of a discrete-time piecewise affine (PWA) systems with time-delay. An H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> state feedback controller design is proposed, and the PWA system was described as ellipsoid which characterized by a set of vector inequalities..thereby the constraint of linear matrix inequalities (LMIs) was released. In terms of LMIs, the time-delay PWA system was stabilized in Lyapunov theory, and the minimum problem of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance index can be cast as a convex optimization problem with LMIs constraints. The simulation results verified the effectiveness of the proposed method.

This paper describes a learning-based approach to operating safety-critical control systems. A reference governor is an add-on scheme used to guard the nominal system against violation of pre-specified constraints by modifying set-point commands. A learning algorithm is developed in this paper to evolve the reference governor parametrization to gradually improve its performance in terms of response speed. In particular, the learning algorithm does not rely on an explicit model of the control system, i.e., it is model-free, and guarantees constraint satisfaction for all time, both during and after learning. The approach is applied to a case study of ground vehicle rollover avoidance to illustrate its functionality and characteristics.

In this paper, we present a model based on copositive programming and semidefinite relaxations of it to prove properties on discrete-time piecewise affine systems. We consider invariant i.e. properties represented by a set and formulated as all reachable values are included in the set. Also, we restrict the analysis to sublevel sets of quadratic forms i.e. ellipsoids. In this case, to check the property is equivalent to solve a quadratic maximization problem under the constraint that the decision variable belongs to the reachable values set. This maximization problem is relaxed using an abstraction of reachable values set by a union of truncated ellipsoids.

Non-synchronized Observer-based Control of Discrete-time Piecewise Affine Systems: an LMI Approach