117,562 research outputs found
Non-minimal factorization approach to the linf-gain of discrete-time linear systems
No full textA method is presented to compute the l∞-gain of discrete-time linear MIMO systems which is based on
a newly derived sequence of factorizations for G(z ). By resorting to a chain-scattering representation of
the system, the proposed approach offers a criterion enabling one to cope with the static output feedback
l
1-control design by solving a finite set of linear inequalities. Numerical examples are reported as well as
an application to the synthesis of a performing decentralized l
1-controller
Stability, L 1 performance and state feedback design for linear systems in ice-cream cones
No full textThis paper considers linear systems which are positively invariant in a second-order cone (ice-cream cone). Three problems are addressed: (i) stability; (ii) L 1 performance; (iii) state feedback design for stabilisation and optimal L 1 performance while preserving cone invariance. We derive necessary and sufficient conditions via Linear Matrix Inequalities (LMI) for the solution of problems (i) and (ii). As for problem (iii), a full parametrization of feasible state feedback gains is provided, along with some LMI relaxations useful to compute a feasible gain. Finally, a numerical example is briefly discussed
Stability and stabilization of discrete-time semi-Markov jump linear systems via semi-Markov kernel approach
No full textThis paper is concerned with the problems of stability and stabilization for a class of discrete-time semi-Markov jump linear systems (S-MJLSs). The discrete-time semi-Markov kernel (SMK) is introduced, where the probability density function of sojourn-time is dependent on both current and next system mode. As a consequence, different types of distributions and/or different parameters in a same type of distribution of sojourn-time, depending on the target mode towards which the system jumps, can coexist in each mode of a SMK. The underlying S-MJLSs are therefore more general than those considered in existing studies. A new stability concept generalizing the traditional mean square stability is proposed such that numerically testable criteria on the basis of SMK are obtained. Numerical examples are presented to illustrate the validity and advantage of the developed theoretical results
Stability and Stabilization of Semi-Markov Jump Linear Systems with Exponentially Modulated Periodic Distributions of Sojourn Time
No full textThis paper is concerned with a class of discrete-time semi-Markov jump linear systems (S-MJLSs) subject to exponentially modulated periodic (EMP) probability density function (PDF) of sojourn time, and the problems of stability and stabilization are addressed. Setting a relatively large period, the considered systems are capable of approximating the general S-MJLSs (without any requirements on sojourn-time PDFs) for which numerically testable stability and stabilization conditions are rather difficult to obtain. Necessary and sufficient criterion for mean square stability of the general S-MJLSs is first derived, which involves an infinite number of conditions and as such not checkable. However, the developments lay a foundation to further establish the numerically testable conditions for the systems when the PDF of sojourn time is EMP albeit the sojourn time can tend to infinity. The derivations explicitly depend on the PDF of sojourn time, which circumvents the difficulty in obtaining the memory transition probabilities of S-MJLSs. The adopted Lyapunov function is sojourn-time-dependent (STD), by which the existence conditions of STD controller are developed as well using certain techniques that can eliminate the terms of power of matrices in the stability conditions. Two illustrative examples including a class of population ecological systems are presented to show the validity and applicability of the developed theoretical results
Mean-Field Game for Collective Decision-Making in Honeybees via Switched Systems
No full textIn this article, we study the optimal control problem arising from the mean-field game formulation of the collective decision-making in honeybee swarms. A population of homogeneous players (the honeybees) has to reach consensus on one of two options. We consider three states: the first two represent the available options (or strategies), and the third one represents the uncommitted state. We formulate the continuous-time discrete-state mean-field game model. The contributions of this article are the following: 1) we propose an optimal control model where players have to control their transition rates to minimize a running cost and a terminal cost, in the presence of an adversarial disturbance; 2) we develop a formulation of the micro–macro model in the form of an initial-terminal value problem with switched dynamics; 3) we study the existence of stationary solutions and the mean-field Nash equilibrium for the resulting switched system; 4) we show that under certain assumptions on the parameters, the game may admit periodic solutions; and 5) we analyze the resulting microscopic dynamics in a structured environment where a finite number of players interact through a network topology
Minimum-time control of a class of nonlinear systems with partly unknown dynamics and constrained input
No full textThe minimum-time problem frequently arises in the design of control for actuators, and is usually solved assuming to know the correct model of the system. In industrially important cases, however, important parts of the dynamics, like friction forces or disturbances by exosystems, are hardly known or even unknown. Against this background, this paper presents an iterative approach to achieve the minimum-time control for a nonlinear, single input second-order system with constrained input and partly unknown dynamics, effectively removing the requirement of perfect knowledge of the system and its parameters to achieve the minimum-time solution in application. First it is shown that, under reasonable assumptions about the unknown part of the dynamics, the optimal control exists for the presented class of systems and that it is a bang-bang control, with at most one switch. Then this property is exploited in the proposed algorithm, that finds the single optimal switching time by an iterative method, without involving any kind of identification of the unknown system parts
Learning Time Optimal Control of Smart Actuators with Unknown Friction
No full textActive valves are most effective tools to control gas flow in compressors if fast transitions
between the open mode and closed mode are needed. Unfortunately, an accurate model including several
nonlinear effects and in particular the resistance and gas flow forces is not available, and this prevents
the use of standard model based approaches for time optimal control. However, the repetitive nature
of the operation of valves suggests the use of learning methods to track a reference in spite of the
insufficient information on the control behavior, thus shifting the problem from the search of the time
optimal control to the search of the reference corresponding to its solution. To this end, in this paper, a
previously proposed algorithm for the iterative determination of the fastest feasible trajectory is analyzed
in terms of convergence conditions and applied to the valve mode
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