Consistent approximations of the zeno behaviour in affine-type switched dynamic systems

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems

This contribution deals with a robust control design for general switched affine control systems. Dynamical models under consideration are described by ordinary differential equations involving a switching mechanism and in the presence of bounded uncertainties. The design procedure we analyse is based on the newly elaborated attractive ellipsoids method ([32]). The stability and robustness of the resulting closed-loop systeminvolves an abstract Clarke stability theoremand a theoretic extension of the celebrated Lyapunov-typemethodology. A short discussion on the obtained analytic results and possible applications and extensions is also included. © 2017 by Nova Science Publishers, Inc. All Rights Reserved

A first-order numerical approach to switched-mode systems optimization

This paper studies optimal control processes governed by switched-mode systems. We consider Optimal Control Problems (OCPs) with smooth cost functionals and apply a newly elaborated abstraction for the system dynamics under consideration. The control design we finally obtain includes an optimal switching times selection ("timing") as well as an optimal modes sequence scheduling ("sequencing"). For purpose of numerical treatment of the initially given OCP we use a newly elaborated relaxation concept and analyse the resulting "weakly relaxed" optimization problems. In contrast to the conventional relaxations our approach is based on the infimal prox convolution technique and does not use the celebrated Chattering Lemma. This fact causes a lower relaxation gap. Our aim is to propose a gradient-based computational algorithms for the OCPs with switched-mode dynamics. In particular, we deal with the celebrated Armijo-type gradient methods and establish the corresponding convergence properties. The numerical consistency (numerical stability) analysis makes it possible to apply a class of relative simple first-order numerical procedures to a sophisticated initial OCP involved in specific switched-mode dynamics. © 2017 Elsevier Ltd

Convex Control Systems and Convex Optimal Control Problems With Constraints

This note discusses the concepts of convex control systems and convex optimal control problems. We study control systems governed by ordinary differential equations in the presence of state and target constraints. Our note is devoted to the following main question: under which additional assumptions is a “sophisticated” constrained optimal control problem equivalent to a “simple” convex minimization problem in a related Hilbert space. We determine some classes of convex control systems and show that, for suitable cost functionals and constraints, optimal control problems for these classes of systems correspond to convex optimization problems. The latter can be reliably solved using standard numerical algorithms and effective regularization schemes. In particular, we propose a conceptual computational approach based on gradient-type methods and proximal point techniques. © Copyright 2008 IEEE – All Rights Reserved [accessed July 10, 2008