Vladimir Dykhta

Vladimir Dykhta
Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences (ISDCT SB RAS)

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30
Publications
500
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205
Citations

Publications

Publications (30)
Chapter
We consider a non-smooth optimal control problem with Lipschitz dynamics with respect to state variables and a terminal functional, which is defined by a semiconcave function (the difference between smooth and continuous convex functions). For suboptimal processes of this problem, the variational type necessary optimality condition is obtained. Thi...
Article
Full-text available
We consider an optimal impulsive control problem with a terminal functional and trajectories of bounded variation. The control system we consider has a bilinear structure with respect to the state and control variables and is governed by nonnegative vector Borel measures under constraints on their total variation. This problem is the impulsive-traj...
Article
We derive nonlocal necessary optimality conditions, which efficiently strengthen the classical Pontryagin maximum principle and its modification obtained by B. Kaśkosz and S. Łojasiewicz as well as our previous result of a similar kind named the “feedback minimum principle.” The strengthening of the feedback minimum principle (and, hence, of the Po...
Article
The paper is devoted to the development of the canonical theory of the Hamilton–Jacobi optimality for nonlinear dynamical systems with controls of the vector measure type and with trajectories of bounded variation. Infinitesimal conditions of the strong and weak monotonicity of continuous Lyapunov-type functions with respect to the impulsive dynami...
Article
We obtain necessary global optimality conditions for classical optimal control problems based on positional controls. These controls are constructed with classical dynamical programming but with respect to upper (weakly monotone) solutions of the Hamilton-Jacobi equation instead of a Bellman function. We put special emphasis on the positional minim...
Article
The proximity is estimated of a resource quasioptimal control to the optimal control. We give a method for subdividing the bounded region of initial conditions into subregions and bringing the quasioptimal control closer to the resource optimal control.
Article
This article is devoted to some applications of Hamilton–Jacobi inequalities for control problems of ordinary and impulsive dynamical systems. We focus on the study of necessary and sufficient global optimality conditions. The optimality conditions are obtained by using certain families of Lyapunov type functions, where Lyapunov type functions can...
Article
For linear systems with constrained control and fixed transition time, we propose two methods for solving the resource consumption minimization problem approximately. We prove that the switching moments of resource-quasioptimal controls are independent of the initial conditions and constant for autonomous systems. Some region of the initial conditi...
Article
The canonical theory of the necessary and sufficient conditions for global optimality based on the sets of nonsmooth solutions of the differential Hamilton-Jacobi inequalities of two classes of weakly and strongly monotone Lyapunov type functions was developed. These functions enable one to estimate from above and below the objective functional of...
Conference Paper
Sufficient and necessary global optimality conditions for nonlinear impulsive dynamic optimization problems with endpoints constraints are obtained. Proofs of these results are based on Hamilton-Jacobi canonical optimality theory. As consequence, a Maximum Principle reverse into sufficient optimality conditions is proposed.
Article
We develop a canonical global optimality theory based on operating with the set of solutions for the Hamilton-Jacobi inequalities that parametrically depend on the initial (or final) position. These solutions, called positional L-functions (of Lyapunov type), naturally arise in the studies of control problems for discrete-continuous (hybrid, impuls...
Article
We propose definitions of strong and weak monotonicity of Lyapunov-type functions for nonlinear impulsive dynamical systems that admit vector measures as controls and have trajectories of bounded variation. We formulate infinitesimal conditions for the strong and weak monotonicity in the form of systems of proximal Hamilton-Jacobi inequalities. As...
Article
A nonlinear optimal impulsive control problem with trajectories of bounded variation subject to intermediate state constraints at a finite number on nonfixed instants of time is considered. Features of this problem are discussed from the viewpoint of the extension of the classical optimal control problem with the corresponding state constraints. A...
Article
This paper surveys theoretical results on the Pontryagin maximum principle (together with its conversion) and nonlocal optimality conditions based on the use of the Lyapunov-type functions (solutions to the Hamilton-Jacobi inequalities). We pay special attention to the conversion of the maximum principle to a sufficient condition for the global and...
Article
Full-text available
First-order and second-order necessary conditions of optimality for an impulsive control problem that remain informative for abnormal control processes are presented and derived. One of the main features of these conditions is that no a priori normality assumptions are required. This feature follows from the fact that these conditions rely on an ex...
Article
In this article, we present first and second order necessary conditions of optimality for impulsive control problems recently obtained by the authors. Two kind of results are discussed: first order necessary conditions of optimaiity for the free time optimal control problem with state and control constraints and second order necessary conditions fo...
Article
The paper discusses sufficient optimality conditions for optimal control problems with linear unbounded or semibounded controls. These problems admit a natural extension associated with the transition to generalized discontinuous trajectories and impulse controls. Possibilities of applying sufficient optimality conditions based on the use of the se...
Conference Paper
Full-text available
We present first and second order necessary conditions of optimality for a general class of nonlinear measure driven dynamic control systems subject to both equality and inequality endpoint state constraints. An important feature of our result is that the conditions remain informative even for abnormal control processes. Our result is obtained by d...
Article
A necessary condition of optimality—the variational maximum principle—for continuous dynamic optimization problems under linear unbounded control and trajectory terminal constraints is studied. It holds for optimal control problems, which are characterized by the commutativity of vector fields corresponding to the components of a linear control in...
Article
Full-text available
In this communication, we discuss necessary conditions of optimality for impul-sive control problems. That is, problems whose control space includes measures besides the conventional class of measurable functions. More precisely, we present second-order necessary conditions of optimality for control problems with equality and inequality endpoint st...

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