On the existence of optimal processes
On the properties of the Aumann integral with applications to differential inclusions and control systems
On the theory of functional-differential inclusions of neutral type.
On Theoretical and Numerical Aspects of the Bang-Bang-Principle.
Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics
This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...
Optimality and sensitivity for semilinear bang-bang type optimal control problems
In optimal control problems with quadratic terminal cost functionals and systems dynamics linear with respect to control, the solution often has a bang-bang character. Our aim is to investigate structural solution stability when the problem data are subject to perturbations. Throughout the paper, we assume that the problem has a (possibly local) optimum such that the control is piecewise constant and almost everywhere takes extremal values. The points of discontinuity are the switching points. In...
Optimality and stability result for bang-bang optimal controls with simple and double switch behaviour
Optimality properties of controls with bang-bang components in problems with semilinear state equation
Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines
2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.
Second order conditions for bang-bang control problems
Seeking bang-bang solutions of mixed immuno-chemotherapy of tumors.
Sous-solutions pour un problème unilatéral d'évolution : caractérisation et régularité
The existence theorem for one class of optimal problems in Banach space.
The optimal control chart procedure
The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span is specified by a partition of the space into three disjoint parts. We call this partition as the control chart frame of span A shift in the process parameter is signalled at time by having the vector of the last sample characteristics fall out of the...
The shooting approach in analyzing bang-bang extremals with simultaneous control switches
The structure of the critical set in the general mountain pass principle
The sufficient condition for linear constant time-lag systems to be normal systems
Time optimal control of a second order nonlinear plant
Time optimal control of the heat equation with pointwise control constraints
Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained....
Time optimal control problem for differential inclusions