Mato Baotić

Multi-Parametric Toolbox (MPT)

A Multi-Parametric Toolbox (MPT) for computing optimal or suboptimal feedback controllers for constrained linear and piecewise affine systems is under development at ETH. The toolbox offers a broad spectrum of algorithms compiled in a user friendly and accessible format: starting from different performance objectives (linear, quadratic, minimum time) to the handling of systems with persistent additive disturbances and polytopic uncertainties. The algorithms included in the toolbox are a collection of results from recent publications in the field of constrained optimal control of linear and piecewise affine systems [10,13,4,9,16,17,15,14,7].

Dynamic programming for constrained optimal control of discrete-time linear hybrid systems

In this paper we study the solution to optimal control problems for constrained discrete-time linear hybrid systems based on quadratic or linear performance criteria. The aim of the paper is twofold. First, we give basic theoretical results on the structure of the optimal state-feedback solution and of the value function. Second, we describe how the state-feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming.

Stabilizing low complexity feedback control of constrained piecewise affine systems

Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin. This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction.

Efficient On-Line Computation of Constrained Optimal Control

We consider constrained finite-time optimal control problems for discrete-time linear time-invariant systems with constraints on inputs and outputs based on linear and quadratic performance indices. The solution to such problems is a time-varying piecewise affine (PWA) state-feedback law and can be computed by means of multiparametric programming. By exploiting the properties of the value function and the piecewise affine optimal control law of the constrained finite-time optimal control (CFTOC), we propose two new algorithms that avoid storing the polyhedral regions. The new algorithms significantly reduce the on-line storage demands and computational complexity during evaluation of the PWA feedback control law resulting from the CFTOC.

Hybrid Theory-Based Time-Optimal Control of an Electronic Throttle

An electronic throttle is a dc-motor-driven valve that regulates air inflow into the combustion system of the engine. The throttle control system should ensure fast and accurate reference tracking of the valve plate angle while preventing excessive wear of the throttle components by constraining physical variables to their normal-operation domains. These high-quality control demands are hard to accomplish since the plant is burdened with strong nonlinear effects of friction and limp-home nonlinearity. In this paper, the controller synthesis is performed in discrete time by solving a constrained time-optimal control problem for the piecewise affine (PWA) model of the throttle. To that end, a procedure is proposed to model friction in a discrete-time PWA form that is suitable both for simulation and controller design purposes. The control action computation can, in general, be restated as a mixed-integer program. However, due to the small sampling time, solving such a program online (in a receding horizon fashion) would be very prohibitive. This issue is resolved by applying recent theoretical results that enable offline precomputation of the state-feedback optimal control law in the form of a lookup table. The technique employs invariant set computation and reachability analysis. The experimental results on a real electronic throttle are reported and compared with a tuned PID controller that comprises a feedforward compensation of the process nonlinearities. The designed time-optimal controller achieves considerably faster transient, while preserving other important performance measures, like the absence of overshoot and static accuracy within the measurement resolution

An efficient algorithm for computing the state feedback optimal control law for discrete time hybrid systems

In this paper we propose an efficient algorithm for computing the solution to the finite time optimal control problem for discrete time linear hybrid systems with a quadratic performance criterion. The algorithm is based on a dynamic programming recursion and a multiparametric quadratic programming solver.

Hybrid Systems Modeling and Control

Piece-wise affine and mixed logical dynamical models for discrete time linear hybrid systems are reviewed. Constrained optimal control problems with linear and quadratic objective functions are defined. Some results on the structure and computation of the optimal control laws are presented. The effectiveness of the techniques is illustrated on a wide range of practical applications.

Constrained Optimal Control of Hybrid Systems With a Linear Performance Index

We consider the constrained finite and infinite time optimal control problem for the class of discrete-time linear hybrid systems. When a linear performance index is used the finite and infinite time optimal solution is a piecewise affine state feedback control law. In this paper, we present algorithms that compute the optimal solution to both problems in a computationally efficient manner and with guaranteed convergence and error bounds. Both algorithms combine a dynamic programming exploration strategy with multiparametric linear programming and basic polyhedral manipulation

Optimal control of piecewise affine systems : A dynamic programming approach

We consider the constrained finite and infinite time optimal control problem for the class of discrete-time linear piecewise affine systems. When a linear performance index is used the finite and infinite time optimal solution is a piecewise affine state feedback control law. In this paper we present an algorithm to compute the optimal solution for the finite time case where the algorithm combines a dynamic programming exploration strategy with multi-parametric linear programming and basic polyhedral manipulation. We extend the ideas to the infinite time case and show the equivalence of the dynamic programming generated solution with the solution to the infinite time optimal control problem.

Multi-object adaptive cruise control

In this paper we propose an algorithm for solving a Multi-Object Adaptive Cruise Control problem.In a multi-object traffic scene the optimal acceleration is to be found respecting traffic rules, safety distances and driver intentions.The objective function is modelled as a quadratic cost function for the discrete time piecewise affine system. We find the optimal state-feedback control law by solving the underlying constrained finite time optimal control problem via dynamic programming.