Exponential Stabilisation of Continuous-time Periodic Stochastic Systems by Feedback Control Based on Periodic Discrete-time Observations

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, time-varying observation frequencies have not been considered. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodic time-varying frequencies. This study investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This study provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for p > 1 and almost sure exponential stability. Lyapunov's method and inequalities are main tools for derivation and analysis. The existence of observation interval sequences is verified and one way of its calculation is provided. Finally, an example is given for illustration. Their new techniques not only reduce observational cost by reducing observation frequency dramatically but also offer flexibility on system observation settings. This study allows readers to set observation frequencies according to their needs to some extent

Multi-Objective Robust H-infinity Control of Spacecraft Rendezvous

Based on the relative motion dynamic model illustrated by C-W equations, the problem of robust Hinfin control for a class of spacecraft rendezvous systems is investigated, which contains parametric uncertainties, external disturbances and input constraints. An Hinfin state-feedback controller is designed via a Lyapunov approach, which guarantees the closed-loop system to meet the multi-objective design requirements. The existence conditions for admissible controllers are formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimization problem subject to LMI constraints. An illustrative example is provided to show the effectiveness of the proposed control design method

Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed

Differential games through viability theory : old and recent results.

This article is devoted to a survey of results for differential games obtained through Viability Theory. We recall the basic theory for differential games (obtained in the 1990s), but we also give an overview of recent advances in the following areas : games with hard constraints, stochastic differential games, and hybrid differential games. We also discuss several applications.Game theory; Differential game; viability algorithm;

Online identification and nonlinear control of the electrically stimulated quadriceps muscle

A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure

Path-wise control of stochastic systems: overcoming the curse of causality

In this thesis we address the topic of path-wise control of stochastic systems defined by stochastic differential equations. By path-wise control we mean that the controller's decisions are not intended to regulate the moments of the state or the output (or a function of them), as customary in stochastic control. Instead, we aim at designing a controller that achieves a desired, specific, trajectory of the state (or the output) itself, for all possible realisations of the noise affecting the system. We show that path-wise control is cursed by insuperable causality issues, because in order to perfectly attain a predefined trajectory for each realisation of the noise, the controller needs to access measurements of the noise itself, which is not possible in practice. Therefore, we approach path-wise control in two steps. Firstly, we design idealistic controllers, which achieve exact regulation by employing a feedback of the noise. Although unrealistic, these designs are preliminary to the second step, i.e. the construction of practical controllers, which estimate the noise from measurements of available quantities (state or output) and use such estimates to perform approximate path-wise control in a hybrid way. We show that the performance of the practical controllers can retrieve the idealistic ones in a limit behaviour. In this framework we address two classical control problems. Firstly, we consider output regulation of linear stochastic systems. We show that the idealistic controllers achieve a zero steady-state tracking error, while the practical controllers allow for a nonzero steady-state error, which, however, can be made arbitrarily small by tuning a design parameter. Secondly, we consider the control of stochastic systems defined by nonlinear, control-affine, stochastic differential equations. In this case, we show that the idealistic controllers achieve exact feedback linearisation and output tracking, while the practical controllers achieve state (and output) trajectories which can be made close to the idealistic ones by tuning a design parameter, thus obtaining approximate feedback linearisation and tracking.Open Acces