Dmitry Gromov

Necessary optimality conditions for a class of hybrid optimal control problems

In this paper we study a class of Mayer-type hybrid optimal control problems. Using Lagrange techniques, we formulate a version of the Hybrid Maximum Principle for optimal control problems governed by hybrid systems with autonomous location transitions in the presence of additional target constraints.

Stability of interconnected thermodynamic systems

In this paper, a formulation of thermodynamic systems in terms of contact geometry is proposed and a systematic approach to the description of interconnected thermodynamic systems is developed. The paper presents a number of results on the stability of interconnected thermodynamic systems.

Optimal hybrid control for switched affine systems under safety and liveness constraints

In this contribution, we propose a two-level hierarchical control strategy to solve the problem of minimising a cost function for a switched affine system under safety and liveness constraints. The constraints are handled on the lower level by a discrete supervisory controller designed using l-complete approximation. Its action can be represented as state invariants added to the plant model. In a bottom-up strategy, we can then synthesis a high-level controller, which computes a set of switching tables using the remaining degrees of freedom to optimise a quadratic performance index

INTERCONNECTION OF THERMODYNAMIC CONTROL SYSTEMS

Abstract In this paper, we propose a formulation of thermodynamic systems in terms of contact geometry and develop a systematic approach to the description of their evolution. In particular, we extend our results to the case of interconnected thermodynamic systems.

Implicit and explicit representations of continuous-time port-Hamiltonian systems

Implicit and explicit representations of smooth, nite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations. Explicit representations are derived when generalized coordinates are used. A relationship between the phase spaces for both system representations is derived in this article, justifying the equivalence of the representations in the sense of preserving their Hamiltonian functions as well as their Hamiltonian symplectic forms, ultimately resulting in the same Hamiltonian ow.

Timed Discrete Event Control of Parallel Production Lines with Continuous Outputs

In this contribution we present an approach to formulate and solve certain scheduling tasks for hybrid systems using timed discrete event control methods. To demonstrate our approach, we consider a cyclically operated plant with parallel reactors using common resources and a continuous output. For this class of systems, we show how to pose the control problem within a discrete event framework by modelling system components as multirate timed automata. We propose a supervisory control strategy incorporating off-line optimisation to assure safety and nonconflicting use of resources. These properties have to be achieved in the presence of a class of bounded errors/disturbances and can be verified by applying formal methods.

DETECTING AND ENFORCING MONOTONICITY FOR HYBRID CONTROL SYSTEMS SYNTHESIS

Abstract Abstraction based approaches to control of hybrid systems require efficient means of computing outer approximations of reachable continuous state sets. This contribution discusses how the concept of monotonicity can be used for this purpose. It provides an efficient algorithm to check whether a given continuous system is monotone with respect to a (a-priori unknown) partial order and, if not, investigates how to use continuous feedback to enforce monotonicity. In the latter case, the resulting continuous feedback represents a (lower) control level within a hierarchical hybrid control system.

On a Class of Hybrid Differential Games

This paper is intended to present a systematic application of the hybrid systems framework to differential games. A special class of bimodal linear-quadratic differential games is presented and illustrated with examples; two particular classes of switching rules, time-dependent and state-dependent switches are discussed. The main contribution of the paper consists in formulating necessary optimality conditions for determining optimal strategies in both cooperative and non-cooperative cases. A practically relevant hybrid differential game of pollution reduction is considered to illustrate the developed framework.

TIMED DISCRETE EVENT CONTROL OF A PARALLEL PRODUCTION LINE WITH CONTINUOUS OUTPUT

Abstract In this paper we present an approach to formulate and solve certain scheduling tasks using timed discrete event control methods. To demonstrate our approach, we consider a special class of systems: a cyclically operated chemical plant with parallel reactors using common resources and a continuous output. This problem was motivated by a benchmark proposed within the EU Network of Excellence HYCON. For this class of systems, we show how to pose the control problem within a discrete event framework by modelling system components as multirate timed automata. Safety and nonblocking are investigated. These properties have to be achieved in the presence of a class of bounded errors/disturbances.

Passivity-based control of implicit port-Hamiltonian systems with holonomic constraints

Abstract Implicit port-Hamiltonian representations of mechanical systems are considered from a control perspective. Energy shaping is used for the purpose of stabilizing a desired equilibrium. When using implicit models, the problem turns out to be a simple quadratic programming problem (as opposed to the partial differential equations that need to be solved when using explicit representations). The described approach is generalized to address the problem of stabilization of homoclinic orbits thus leading to the formulation of swing-up strategies for underactuated systems.