Robust reliable H-infinity control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters

This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional（LKF）, sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities（LMIs）. The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.

A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

Robust and Non-fragile H_∞ Control for a Class of Uncertain Jump Linear Systems

This paper describes the synthesis of robust and non-fragile H∞ state feedback controllers for a class of uncertain jump linear systems with Markovian jumping parameters and state multiplicative noises. Under the assumption of a complete access to the norm-bounds of the system uncertainties and controller gain variations, sufficient conditions on the existence of robust stochastic stability and γ-disturbance attenuation H∞ property are presented. A key feature of this scheme is that the gain matrices of controller are only based on It, the observed projection of the current regime rt.

Synchronization of Markovian jumping complex networks with event-triggered control

This paper investigates event-triggered synchronization for complex networks with Markovian jumping parameters.Nonlinear dynamics with Markovian jumping parameters is considered for each node in a complex network. By utilizing the proposed event-triggered strategy, and based on the Lyapunov functional method and linear matrix inequality technology,some sufficient conditions for synchronization of complex networks are derived whether the transition rate matrix for the Markov process is completely known or not. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.

Guaranteed control performance robust LQG regulator for discrete-time Markovian jump systems with uncertain noise

Robust LQG problems of discrete-time Markovian jump systems with uncertain noises are investigated. The problem addressed is the construction of perturbation upper bounds on the uncertain noise covariances so as to guarantee that the deviation of the control performance remains within the precision prescribed in actual problems. Furthermore, this regulator is capable of minimizing the worst performance in an uncertain case. A numerical example is exploited to show the validity of the method.

Stochastic stabilization of Markovian jump cloud control systems based on max-plus algebra

In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with a reference signal. For the Markovian jump cloud control system, there exists framework adjustment whose evolution is satisfied with a Markov chain. Using max-plus algebra, a maxplus stochastic system is used to describe the Markovian jump cloud control system. A causal feedback matrix is obtained by exponential stability analysis for a causal feedback controller of the Markovian jump cloud control system. A sufficient condition is given to ensure existence on the causal feedback matrix of the causal feedback controller. Based on the causal feedback controller, stochastic stabilization in probability is analyzed for the Markovian jump cloud control system with a reference signal.Simulation results are given to show effectiveness of the causal feedback controller for the Markovian jump cloud control system.

Stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks with mixed delays and the Wiener process based on sampled-data control

We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks （MJFCNNs） with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality （LMI） approach. The Lyapunov–Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions （e.g., time derivative is smaller than one） are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.

FINITE-TIME H∞ CONTROL FOR A CLASS OF MARKOVIAN JUMPING NEURAL NETWORKS WITH DISTRIBUTED TIME VARYING DELAYS-LMI APPROACH

In this article, we investigates finite-time H∞ control problem of Markovian jumping neural networks of neutral type with distributed time varying delays. The mathematical model of the Markovian jumping neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems. Finite time stability analysis for such neural networks is addressed based on the linear matrix inequality approach. Numerical examples are given to illustrate the usefulness of our proposed method. The results obtained are compared with the results in the literature to show the conservativeness.

Robust reliable H_∞ control for discrete-time Markov jump linear systems with actuator failures

The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures, The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities （LMIs）. A numerical example is also given to illustrate the design procedures and their effectiveness.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

Medial Longitudinal Arch Pad Influences Landing Control of the Lower Limbs during Single-Leg Jump-Landing

Background: Arch support has the effect of maintaining arch and correcting alignment, and it is broadly used for the prevention of sports impediment and treatment of athletes with lowered MLA and foot problems. The fact that the morphological change of MLA damages balance sense and postural control, it was reported that the insole supporting the arch of MLA improved postural balance. There are several studies regarding the effects of arch support;however, its effects on landing control have not been clarified. Therefore, in our research, we discussed the effect of MLA support for landing control, using lower limb dynamic alignment and the moment during landing as indexes. Methods: This study measured the landing motion to be evaluated was to jump from a platform with a height of 30 cm by taking-off with a single foot, and landing on a single foot on a floor reaction force gauge placed ahead and stay still for three seconds for the subjects were 13 healthy females. A soft 6 mm Boron sheet cut in the size of 9 × 3.5 cm, applied with double-sided tape (MLA pad) was used for arch support (hereafter referred to as “pad”). For the lower limb evaluation, an 8-camera with a three-dimensional behavioral analyzer (CORTEX, NAC product, sampling frequency: 120 Hz) and a floor reaction force gauge (AMTI product, sampling frequency: 1000 Hz) were used. Ten successful jump-landing tests for each limb were used for further analyses using Visual 3D software (Cmotion Inc., Kingston, Canada). Analysis objects were knee joint bending angle and valgus angle during landing;knee joint maximum bending angle;bending knee joint valgus angle, hip joint bending angle, adduction angle, ankle joint plantar flexion angle, varus angle at the time of knee joint maximum bending angle;and each joint moment. For statistical processing, the average value of three trials out of five trials was regarded as a representative value. Results: Regarding joint angles, significant differences were observed in maximum knee joint bending angle, knee joint bending angle during maximum valgus knee joint and ankle joint varus angle during knee joint maximum bending angle between before and after intervention. No significant differences were observed in other joint angles. Regarding joint moments, no significant difference was observed in each joint moment before and after the intervention. Significance: The decrease of knee joint valgus angle during landing by the use of MLA pad suggests the possibility of decreasing the risk of ACL injury. As the incidence of ACL injury in females is higher than that of males, and the evaluation for females had proceeded, it can be useful information for the prevention of ACL injury.

Delay-dependent guaranteed cost control for uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays

In this paper,the problem of guaranteed cost control for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays and a given quadratic cost function are investigated. Attention is focused on designing a memoryless state feedback control law such that the closed-loop system is robust stochastically stable and the closed-loop cost function value is not more than a specified upper bound,for all admissible uncertainties. The key features of the approach include the introduction of a new type of suitable stochastic Lyapunov functional and free weighting matrices techniques. Sufficient conditions for the existence of such controller are obtained in terms of a set of linear matrix inequalities. A numerical example is given to illustrate the less conservatism of the proposed techniques.

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm. © 2014 Chinese Association of Automation.

Remotely Controlled Automated Horse Jump

With the application of automation, a horse jump can be controlled with the push of a button, or even a remote control. This enables the rider to adjust the jump to suit their needs while still on their horse. The objective of this work is to design and build a wireless remote motor controller which will be applied to a prototype horse jump. The user will be able to control the forward and reverse direction of the motor by pushing a button or switch via RF remote control. A horse jump prototype consisting of a single jump stand will be constructed.

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.

H_∞ Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters

This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Receding horizon H_∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

基于深度强化学习的液压四足机器人单腿跳跃优化控制

液压四足机器人具有功率密度高、负载能力大等优势,但其液压系统控制参数与机身运动参数间耦合关系复杂且维度较高,导致最优控制参数的求解十分困难。为此,采用具有自适应性、抗扰动性的深度强化学习算法,实现机器人单腿在不同工况下的高效、平稳运动。首先,在MATLAB/Simulink中搭建Spurlos液压四足机器人单腿模型;然后,设计基于五次多项式轨迹规划的强化学习控制器;最终实现针对不同目标任务的机器人单腿优化控制。仿真表明,所提强化学习控制策略能够实现机器人跳跃运动的自适应优化控制,训练后的机器人单腿在复杂环境中展现出较强的自适应性与运动稳定性。