Octavian Pastravanu

Brief paper: Adaptive optimal control for continuous-time linear systems based on policy iteration

In this paper we propose a new scheme based on adaptive critics for finding online the state feedback, infinite horizon, optimal control solution of linear continuous-time systems using only partial knowledge regarding the system dynamics. In other words, the algorithm solves online an algebraic Riccati equation without knowing the internal dynamics model of the system. Being based on a policy iteration technique, the algorithm alternates between the policy evaluation and policy update steps until an update of the control policy will no longer improve the system performance. The result is a direct adaptive control algorithm which converges to the optimal control solution without using an explicit, a priori obtained, model of the system internal dynamics. The effectiveness of the algorithm is shown while finding the optimal-load-frequency controller for a power system.

Controller design and conflict resolution for discrete event manufacturing systems

A modern system theory point of view is offered for the design of sequencing controllers for discrete event manufacturing systems with shared resources, whereby the controller is considered as separate from the workcell. The controller design algorithm is based on the required task sequence and the available resources; it is described by linear (i.e. matrix) and nonlinear logical equations using the negative logic. The controller-workcell interaction expressed both in qualitative and quantitative terms allows a rigorous analysis of shared-resource conflicts. The rule-based controller contains inner loops where no shared-resource conflict resolution is required, and extra control inputs to resolve conflict where needed. An example gives an overview of the applicability of the theoretical results. Compatibility with other analysis/design techniques such as Petri-net-based top-down and bottom-up approaches, logical control, (R,max,+) state equations is also addressed. Three methods of conflict resolution are given and related to current work.<<ETX>>

Policy iteration for continuous-time systems with unknown internal dynamics

In this paper we propose a new adaptive critic scheme for finding on-line the state feedback, infinite-horizon, optimal control solution of linear continuous-time systems using only partial knowledge regarding the system dynamics, i.e. no knowledge regarding the system A matrix is needed. This is in effect an adaptive control scheme for partially unknown systems that converges to the optimal control solution.

Max-type copositive Lyapunov functions for switching positive linear systems

The paper aims to expand the stability analysis framework based on copositive Lyapunov functions (CLFs) for arbitrarily switching positive systems with continuous- or discrete-time dynamics. The first part focuses on max-type CLFs. It provides an algebraic characterization (in terms of weak quasi-linear inequalities), as well as an existence criterion relying on a concrete construction procedure (in terms of Perron-Frobenius eigenstructure). The second part explores the connections between max-type and two other classes of CLFs, namely linear and quadratic-diagonal. New qualitative and quantitative features are revealed for the CLFs belonging to the two mentioned classes.

Modeling of a pressure reducing valve actuator for automotive applications

Significant research effort has been directed towards developing vehicle systems that reduce the energy consumption of an automobile and because pressure control valves are used as actuators in many control applications for automotive systems, a proper dynamic model is necessary. Starting from equations found in literature, where a single stage pressure reducing valve is modelled, in this paper, the concept of modeling a real three land three way solenoid valve actuator for the clutch system in the automatic transmission is presented. Two simulators for an input-output model and a state-space model were developed and these were validated with data provided from experiments with the real valve actuator on a test bench.

Flow-Invariance and Stability Analysis for a Class of Nonlinear Systems with Slope Conditions

New results of qualitative analysis are presented for a class of dynamical systems (including the Hopfield neural networks) whose nonlinearities satisfy certain slope conditions. The main instrument of this analysis consists in the individual monitoring of the statetrajectories by considering time-dependent rectangular sets that are forward invariant with respect to the dynamics of the investigated systems. Particular requirements for the rectangular sets approaching the equilibrium point allow a componentwise exploration of the stability properties, offering additional information with respect to the traditional framework (that expresses a global knowledge, built in terms of norms). Within this context, we are able to point out some important dynamical aspects that remained hidden for other works relying only on the standard tools of stability analysis. The refinement induced by the componentwise point of view is also revealed by two numerical examples.

Linear time-variant systems: Lyapunov functions and invariant sets defined by Hölder norms

Abstract For linear time-variant systems x ˙ ( t ) = A ( t ) x ( t ) , we consider Lyapunov function candidates of the form V p ( x , t ) = | | H ( t ) x | | p , with 1 ≤ p ≤ ∞ , defined by continuously differentiable and non-singular matrix-valued functions, H ( t ) : R + → R n × n . We prove that the traditional framework based on quadratic Lyapunov functions represents a particular case (i.e. p=2) of a more general scenario operating in similar terms for all Holder p-norms. We propose a unified theory connecting, by necessary and sufficient conditions, the properties of (i) the matrix-valued function H(t), (ii) the Lyapunov function candidate Vp(x,t) and (iii) the time-dependent set X p ( t ) = { x ∈ R n | | | H ( t ) x | | p ≤ e − rt } , with r≥0. This theory allows the construction of four distinct types of Lyapunov functions and, equivalently, four distinct types of sets which are invariant with respect to the system trajectories. Subsequently, we also get criteria for testing stability, uniform stability, asymptotic stability and exponential stability. For all types of Lyapunov functions, the matrix-valued function H(t) is a solution to a matrix differential inequality (or, equivalently, matrix differential equation) expressed in terms of matrix measures corresponding to Holder p-norms. Such an inequality (or equation) generalizes the role played by the Lyapunov inequality (equation) in the classical case when p=2. Finally, we discuss the diagonal-type Lyapunov functions that are easier to handle (including the generalized Lyapunov inequality) because of the diagonal form of H(t).

Petri Net Toolbox in control engineering education

The Petri Net Toolbox (PN Toolbox) for MATLAB is a software package that offers instruments for the simulation, analysis and design of untimed, deterministic and stochastic P-/T-timed and stochastic Petri nets (PNs). The facilities available in this toolbox are appropriate for studying the dynamics of many classes of discrete-event systems. The Petri Net Simulink Block (PNSB) allows the modeling and analysis of hybrid systems whose event-driven part(s) is (are) modeled based on the PN formalism. The current paper focuses on the exploitation of the PN Toolbox for illustrating the usage of the PN theory in Control Engineering from the pedagogic point of view, the discussion being supported by example problems and comments on the teaching goals. The PN Toolbox is included in the Connections Program of The MathWorks Inc., as a third party product.

MATLAB Tools for Petri-Net-Based Approaches to Flexible Manufacturing Systems

Abstract The skeleton and the functionality of a Petri Net Toolbox, embedded in the MATLAB environment, are briefly presented, as offering a collection of instruments devoted to simulation, analysis and synthesis of discrete-event systems. The integration with the MATLAB philosophy responds to the general interest manifested by educators for enlarging the compatibility between the traditional background of Control Engineering students and the novelty of Discrete-Event-Systems scenarios. Two amply commented case studies illustrate the usage of some facilities available in this new toolbox and prove its capability to cover a wide range of teaching goals for the Petri-net-based approaches to Flexible Manufacturing Systems.

DIAGONALLY-INVARIANT EXPONENTIAL STABILITY

Abstract The diagonally-invariant exponential stability (DIES) is introduced as a special type of exponential stability (ES) which incorporates information about the sets invariant with respect to the state-space trajectories. DIES is able to unify, at the conceptual level, issues in stability analysis that have been separately addressed by previous researches Unlike ES, DIES is a norm-dependent property and its study requires appropriate instruments. These instruments are derived in terms of matrix measures from the characteristics of the system trajectories; their convenient exploitation in practice is ensured by methods based on matrix comparisons. The developed framework presents a noticeable generality and its applicability is illustrated for several classes of linear and non-linear systems. This framework can be simply adapted to discrete-time systems.