Miroslav Baric

Parameterized Robust Control Invariant Sets for Linear Systems: Theoretical Advances and Computational Remarks

We characterize a family of parametrized robust control invariant sets for linear discrete time systems subject to additive but bounded state disturbances. The existence of a member of the introduced family of parametrized robust control invariant sets can be verified by solving a tractable convex optimization problem in the linear convex case, which reduces to the standard linear or convex quadratic programme in the linear polytopic case. The developed method can also be utilized to detect and obtain an implicit representation of local control Lyapunov functions in the linear convex case from the solution of a single and tractable convex optimization problem. The offered method permits for the computation of polytopic robust control invariant sets and local control Lyapunov functions of indirectly controlled and limited complexity in the linear polytopic case.

Recent developments in the control of constrained hybrid systems

We review recently developed schemes for the constrained control of systems integrating logic and continuous dynamics. The control paradigm we focus on is model predictive control (MPC) and its derivatives, with the emphasis on explicit solution. The exposition of the basic theory is supplemented by a number of application case studies showing the effectiveness as well as the limitations of the deployed algorithms. Current and future lines of research are briefly discussed.

Multiparametric Linear Programming with Applications to Control

Parametric programming has received a lot of attention in the control literature in the past few years because model predictive controllers (MPC) can be posed in a parametric framework and hence pro-solved offline, resulting in a significant decrease in on-line computation effort. In this paper we survey recent work on parametric linear programming (pLP) from the point of view of the control engineer. We identify three types of algorithms, two arising from standard convex hull paradigms and one from a geometric intuition, and classify all currently proposed methods under these headings. Through this classification, we identify a third standard convex hull approach that offers significant potential for approximation of pLPs for the purpose of control. We present the resulting algorithm, based on the beneath/beyond paradigm, that computes low-complexity approximate controllers that guarantee stability and feasibility.

Neural network-based sliding mode control of electronic throttle

A neural network-based sliding mode controller for an electronic throttle of an internal combustion engine is proposed. Electronic throttle is modeled as a linear system with uncertainties and affected by disturbances depending on the states of the system. The disturbances, consisting of an unknown friction and a torque caused by the dual spring mechanism inside the mechanical part of the throttle, are estimated by a neural network whose parameters are adapted on-line. The sliding mode controller and the parameters adaptation scheme are derived in order to achieve a tracking of a smooth reference signal, while preserving boundedness of all signals in the closed-loop system. Experimental results are presented which demonstrate the efficiency and robustness of the proposed control scheme.

Technical communique: An efficient algorithm for optimal control of PWA systems with polyhedral performance indices

We present an algorithm for the computation of explicit optimal control laws for piecewise affine (PWA) systems with polyhedral performance indices. The algorithm is based on dynamic programming (DP) and represents an extension of ideas initially proposed in Kerrigan and Mayne [(2003). Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada, USA, December], and Baotic et al. [(2003). A new algorithm for constrained finite time optimal control of hybrid systems with a linear performance index. In Proceedings of European control conference, Cambridge, UK, September]. Specifically, we show how to exploit the underlying geometric structure of the optimization problem in order to significantly improve the efficiency of the off-line computations. An extensive case study is provided, which clearly indicates that the algorithm proposed in this paper may be preferable to other schemes published in the literature.

Robust vehicle lateral stabilisation via set-based methods for uncertain piecewise affine systems

The paper presents the design of a lateral stability controller for ground vehicles based on front steering and four wheels independent braking. The control objective is to track yaw rate and lateral velocity reference signals while avoiding front and rear wheel traction force saturation. Control design is based on an approximate piecewise-affine nonlinear dynamical model of the vehicle. Vehicle longitudinal velocity and drivers steering input are modelled as measured disturbances taking values in a compact set. A time-optimal control strategy which ensures convergence into a maximal robust control invariant (RCI) set is proposed. This paper presents the uncertain model, the RCI computation, and the control algorithm. Experimental tests at high-speed on ice with aggressive driver manoeuvres show the effectiveness of the proposed scheme.

Distributed averaging with flow constraints

A network of storage elements is considered. Each storage element is an integrator which can exchange stored resource with neighboring elements. The flow between the elements as well as the amount of the resource that each element can store are subject to constraints. The problem of averaging the state of each element is addressed. The particularity of this problem compared to standard consensus-based averaging is that the elements exchange not only the information but also the stored resource. Thus the elements are controlled-coupled through the flow constraints. A distributed algorithm for flow control is proposed. The algorithm is non-iterative and does not require centralized design procedure. The proposed scheme guarantees asymptotic convergence of states of all nodes to the same value equal to the average of initial values.

Max–Min Optimal Control of Constrained Discrete-time Systems

Abstract This paper considers the optimal control problem for constrained discrete–time systems affected by measured and bounded disturbances and uncertainties in the underlying system equations. This problem setting leads to the sup–inf robust optimal control problems. Three classes of discrete–time systems permitting the characterization of the sup–inf value functions and robust optimal control policies are examined. The corresponding max–min optimal control problems are solved by using the dynamic programming.

Max-min control problems for constrained discrete time systems

We consider control synthesis problems for constrained discrete time nonlinear systems subject to uncertainty. The uncertainty affects the system in a form of a bounded, but known, persistent disturbance and leads, consequently, to the max-min control synthesis problems. A computational characterization of the max-min controllable sets is derived for a general nonlinear case. The max-min time optimal control of constrained piecewise affine discrete time systems is also discussed. Corresponding computational details are outlined and some illustrative examples are provided.

Neural network based sliding mode controller for a class of linear systems with unmatched uncertainties

This paper considers the application of a neural network for the performance improvement of the sliding mode controller for a class of linear systems with unmatched uncertainties/disturbances. A neural network is employed for the online estimation of the uncertainties using the simple gradient descent learning algorithm. The combination of the sliding mode and backstepping-like recursive control design is used to achieve the desired tracking performance. The algorithm is verified through computer simulations.