Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector

In this paper, we consider the application of the zero-order mini-batch optimization method in the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems in the case of incomplete information about the state vector. The pencil of trajectories originates from a given set of initial states. To solve the problem, the structure of a feedback system is proposed, which contains models of the plant, measuring system, nonlinear state observer and control law of the fixed structure with unknown coefficients. The objective function proposed considers the quality of pencil of trajectories control, which is estimated by the average value of the Bolz functional over the given set of initial states. Unknown control laws of a plant and an observer are found in the form of expansions in terms of orthonormal systems of basis functions, which are specified on the set of possible states of a dynamical system. The original pencil of trajectories control problem is reduced to a global optimization problem, which is solved using the well-proven zero-order method, which uses a modified mini-batch approach in a random search procedure with adaptation. An algorithm for solving the problem is proposed. The satellite stabilization problem with incomplete information is solved.

Set Propagation Techniques for Reachability Analysis

Reachability analysis consists in computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. It is a fundamental problem motivated by many applications in formal verification, controller synthesis, and estimation, to name only a few. This article focuses on a class of methods for computing a guaranteed overapproximation of the reachable set of continuous and hybrid systems, relying predominantly on set propagation; starting from the set of initial states, these techniques iteratively propagate a sequence of sets according to the system dynamics. After a review of set representation and computation, the article presents the state of the art of set propagation techniques for reachability analysis of linear, nonlinear, and hybrid systems. It ends with a discussion of successful applications of reachability analysis to real-world problems. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Safe Reachability Verification of Nonlinear Switched Systems via a Barrier Density

One of the notable temporal properties of dynamical systems is that a set of initial states leads the solutions to reach desired states avoiding a predetermined unsafe set.This property, that we call safe reachability has been studied in literature for autonomous systems using Barrier functionand Barrier densities [1]. In this paper, we generalize a sufficient condition for safe reachability of autonomous systemto switched systems under arbitrary switching signals. The condition relies upon the existence of a common Barrier density function for each subsystem. We apply the condition using the sum of squares method together with Putinar Positivstellensatz.

MCMT in the Land of Parametrized Timed Automata

Timed networks are parametrized systems of timed au\-to\-ma\-ta. Solving reachability problems (e.g., whether a set of unsafe states can ever be reached from the set of initial states) for this class of systems allows one to prove safety properties regardless of the number of processes in the network. The difficulty in solving this kind of verification problems is two-fold. First, each process has (at least one) clock variable ranging over an infinite set, such as the reals or the integers. Second, every system is parameterized with respect to the number of processes and to the topology of the network. Reachability problem for some restricted classes of parameterized timed networks is decidable under suitable assumptions by a backward reachability procedure. Despite these theoretical results, there are few systems capable of automatically solving such problems. Instead, the number $n$ of processes in the network is fixed and a tool for timed automata (like Uppaal) is used to check the desired property for the given $n$.In this paper, we explain how to attack fully parameteric and timed reachability problems by translation to the declarative input language of \textsc{mcmt}, a model checker for infinite state systems based on Satisfiability Modulo Theories techniques. We show the success of our approach on a number of standard algorithms, such as the Fischer protocol. Preliminary experiments show that fully parametric problems can be more easily solved by \textsc{mcmt} than their instances for a fixed (and large) number of processes by other systems.

Planning with Preferences

Automated Planning is an old area of AI that focuses on the development of techniques for finding a plan that achieves a given goal from a given set of initial states as quickly as possible. In most real-world applications, users of planning systems have preferences over the multitude of plans that achieve a given goal. These preferences allow to distinguish plans that are more desirable from those that are less desirable. Planning systems should therefore be able to construct high-quality plans, or at the very least they should be able to build plans that have a reasonably good quality given the resources available.In the last few years we have seen a significant amount of research that has focused on developing rich and compelling languages for expressing preferences over plans. On the other hand, we have seen the development of planning techniques that aim at finding high-quality plans quickly, exploiting some of the ideas developed for classical planning. In this paper we review the latest developments in automated preference-based planning. We also review various approaches for preference representation, and the main practical approaches developed so far.

FRACTALS IN AN ELECTRONIC CIRCUIT WITH BY SWITCHING INPUTS

We have proposed a process of generating fractals not from the results of chaotic dynamics, but from the switching of ordinary differential equations. This paper experimentally and numerically analyzes the dynamics of an electronic circuit driven by stochastically switching inputs. The following two results are obtained. First, the dynamics is characterized by a set Γ(C) of trajectories in the cylindrical phase space, where C is a set of initial states on the Poincaré section. Γ(C) and C are attractive and unique invariant fractal sets that satisfy specific equations. The second result is that the correlation dimension of C is in inverse proportion to the interval of the switching inputs. These two findings move beyond the conventional theory based on contraction maps. It should be noted that the set C is constructed by noncontraction maps.

EXPERIMENTAL VERIFICATION FOR FRACTAL TRANSITION USING A FORCED DAMPED OSCILLATOR

A damped oscillator stochastically driven by temporal forces is experimentally investigated. The dynamics is characterized by a set Γ(C) of trajectories in a cylindrical space, where C is a set of initial states on the Poincaré section. Two sets, Γ(C) and C, are attractive and unique invariant fractal sets that approximately satisfy specific equations derived previously by the authors. The correlation dimension of the set C is in good agreement with the similarity dimension obtained for a strictly self-similar set constructed by contraction mappings while C is a self-affine set constructed by non-contraction mappings.