We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment policies. Our algorithms have competitive performance with the added benefit of...

An analytical investigation of a half-car model with passenger dynamics, subjected to random road disturbance, is performed. Two diierent methods of deening the performance index for optimal controller design are proposed. Nondeterministic inputs are applied to simulate the road surface conditions more realistically. Results obtained illustrate that using an optimal state-feedback controller, w...

The controllability theory may at times lead to a control law as can be seen in the control theory literature. In this paper, a global control algorithm is proposed for nonlinear systems in the so-called linear-analytic form in the plane. The algorithm is motivated by a theorem by Hunt, which gives sufficient conditions for the global controllability of linearanalytic systems on a 2-dimensional...

In this contribution we discuss central and autonomous control of production networks. We provide a number of parameters that influence the comparative effectiveness of these two methods. Further, the results concerning stability of the production networks are discussed and it is shown, how the central planning methods, implemented into mathematical models with the help of optimal control theor...

Although adaptive control theory offers mathematical tools to achieve required system performance without excessive dependence on modeling, its application to safety-critical systems can be limited by the presence of unmodeled dynamics. This paper examines the robustness to unmodeled dynamics of a recently developedderivativefree adaptive control law. In contrast to derivative-based adaptive la...

Anti-angiogenic therapy is a novel treatment approach in cancer therapy that aims at preventing a tumor from developing its own blood supply system that it needs for growth. In this paper a mathematical model for anti-angiogenic treatments based on a biologically validated model by Hahnfeldt, Panigrahy, Folkman and Hlatky is analyzed as an optimal control problem and a full solution of the prob...

We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). The classical approach to DTDGs involves analyzing the problem using optimal control theory which yields results mainly limited to linear-quadratic games [1]. We show the existence of equilibria for a class of DTDGs where the cost function of players ad...

The solution for the above formulated problems are well known (Anderson, Moore, 1990), (Kuo, 1992), but there are some difficulties in implementation of the algorithms. The solution to the P1 problem is usually presented as an open loop control u(k) because the feedback control u(x(k)) has a complicated form. The P2 problem is the most frequently meet linear quadratic problem with finite final ...

We summarize some basic result in dynamic optimization and optimal control theory, focusing on some economic applications.

The paper aims at providing a switching solution for a parametrized Belgian chocolate stabilization problem posed by Blondel. We show that for any given value of the parameter describing the given transfer function, there exist simple switching and periodic control laws that stabilize the plant. The simplicity in designing these control laws sharply contrasts with the difficulty of designing a ...