Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints

The hybrid joints of manipulators can be switched to either active (actuated) or passive (underactuated) mode as needed. Consider the property of hybrid joints, the system switches stochastically between active and passive systems, and the dynamics of the jump system cannot stay on each trajectory errors region of subsystems forever; therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this paper, we consider stochastic stability and sliding mode control for mobile manipulators using stochastic jumps switching joints. Adaptive parameter techniques are adopted to cope with the effect of Markovian switching and nonlinear dynamics uncertainty and follow the desired trajectory for wheeled mobile manipulators. The resulting closed-loop system is bounded in probability and the effect due to the external disturbance on the tracking errors can be attenuated to any preassigned level. It has been shown that the adaptive control problem for the Markovian jump nonlinear systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Finally, a numerical example is given to show the potential of the proposed techniques

Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System

A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme

Development of Novel Compound Controllers to Reduce Chattering of Sliding Mode Control

The robotics and dynamic systems constantly encountered with disturbances such as micro electro mechanical systems (MEMS) gyroscope under disturbances result in mechanical coupling terms between two axes, friction forces in exoskeleton robot joints, and unmodelled dynamics of robot manipulator. Sliding mode control (SMC) is a robust controller. The main drawback of the sliding mode controller is that it produces high-frequency control signals, which leads to chattering. The research objective is to reduce chattering, improve robustness, and increase trajectory tracking of SMC. In this research, we developed controllers for three different dynamic systems: (i) MEMS, (ii) an Exoskeleton type robot, and (iii) a 2 DOF robot manipulator. We proposed three sliding mode control methods such as robust sliding mode control (RSMC), new sliding mode control (NSMC), and fractional sliding mode control (FSMC). These controllers were applied on MEMS gyroscope, Exoskeleton robot, and robot manipulator. The performance of the three proposed sliding mode controllers was compared with conventional sliding mode control (CSMC). The simulation results verified that FSMC exhibits better performance in chattering reduction, faster convergence, finite-time convergence, robustness, and trajectory tracking compared to RSMC, CSMC, and NSFC. Also, the tracking performance of NSMC was compared with CSMC experimentally, which demonstrated better performance of the NSMC controller

Adaptive learning nonsynchronous control of nonlinear hidden Markov jump systems with limited mode information

In this paper, an adaptive neural network learning based nonsynchronous control method is developed for hidden Markov jump systems with unmodeled nonlinear dynamics. In particular, the system modes are not directly accessible and the limited mode information can be partly estimated by the nonsynchronous controller. More precisely, the mode information with partly accessible transition rates is utilized based on the transition probability matrix. Moreover, the unmodeled nonlinear dynamics are more general in practical applications. Based on the designed mode-dependent controllers with mode observation, sufficient conditions are first exploited by means of the Lyapunov method, such that the desired control performance could be ensured in the mean-square sense. Then, the nonsynchronous mode-dependent controllers are further determined in terms of convex optimization. In the end, our proposed control strategy is applied to a robotic manipulator with varying loads to validate the feasibility with simulation results

An integral sliding-mode parallel control approach for general nonlinear systems via piecewise affine linear models

The fundamental problem of stabilizing a general nonaffine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding-mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a nonaffine continuous-time nonlinear system equivalently on a compact region containing the origin. A piecewise sliding-mode parallel controller is designed to globally stabilize the PALM and, consequently, to semiglobally stabilize the original nonlinear system. The proposed scheme enjoys three favorable features: (i) some restrictions on the system input channel are eliminated, thus the developed method is more relaxed compared with the published approaches; (ii) it is convenient to be used to deal with both matched and unmatched uncertainties of the system; and (iii) the proposed piecewise parallel controller generates smooth control signals even around the boundaries between different subspaces, which makes the developed control strategy more implementable and reliable. Moreover, we provide discussions about the universality analysis of the developed control strategy for two kinds of typical nonlinear systems. Simulation results from two numerical examples further demonstrate the performance of the developed control approach

Performance-Driven Robust Identification and Control of Uncertain Dynamical Systems

The grant DEFG02-97ER13939 from the Department of Energy has supported our research program on robust identification and control of uncertain dynamical systems, initially for the three-year period June 15, 1997-June 14, 2000, which was then extended on a no-cost basis for another year until June 14, 2001. This final report provides an overview of our research conducted during this period, along with a complete list of publications supported by the Grant. Within the scope of this project, we have studied fundamental issues that arise in modeling, identification, filtering, control, stabilization, control-based model reduction, decomposition and aggregation, and optimization of uncertain systems. The mathematical framework we have worked in has allowed the system dynamics to be only partially known (with the uncertainties being of both parametric or structural nature), and further the dynamics to be perturbed by unknown dynamic disturbances. Our research over these four years has generated a substantial body of new knowledge, and has led to new major developments in theory, applications, and computational algorithms. These have all been documented in various journal articles and book chapters, and have been presented at leading conferences, as to be described. A brief description of the results we have obtained within the scope of this project can be found in Section 3. To set the stage for the material of that section, we first provide in the next section (Section 2) a brief description of the issues that arise in the control of uncertain systems, and introduce several criteria under which optimality will lead to robustness and stability. Section 4 contains a list of references cited in these two sections. A list of our publications supported by the DOE Grant (covering the period June 15, 1997-June 14, 2001) comprises Section 5 of the report

Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns

In this paper, a backpropagating constraints-based trajectory tracking control (BCTTC) scheme is addressed for trajectory tracking of a quadrotor with complex unknowns and cascade constraints arising from constrained actuator dynamics, including saturations and dead zones. The entire quadrotor system including actuator dynamics is decomposed into five cascade subsystems connected by intermediate saturated nonlinearities. By virtue of the cascade structure, backpropagating constraints (BCs) on intermediate signals are derived from constrained actuator dynamics suffering from nonreversible rotations and nonnegative squares of rotors, and decouple subsystems with saturated connections. Combining with sliding-mode errors, BC-based virtual controls are individually designed by addressing underactuation and cascade constraints. In order to remove smoothness requirements on intermediate controls, first-order filters are employed, and thereby contributing to backstepping-like subcontrollers synthesizing in a recursive manner. Moreover, universal adaptive compensators are exclusively devised to dominate intermediate tracking residuals and complex unknowns. Eventually, the closed-loop BCTTC system stability can be ensured by the Lyapunov synthesis, and trajectory tracking errors can be made arbitrarily small. Simulation studies demonstrate the effectiveness and superiority of the proposed BCTTC scheme for a quadrotor with complex constrains and unknowns

Optimization of the Parameters of RISE Feedback Controller Using Genetic Algorithm

A control methodology based on a nonlinear control algorithm and optimization technique is presented in this paper. A controller called “the robust integral of the sign of the error” (in short, RISE) is applied to control chaotic systems. The optimum RISE controller parameters are obtained via genetic algorithm optimization techniques. RISE control methodology is implemented on two chaotic systems, namely, the Duffing-Holms and Van der Pol systems. Numerical simulations showed the good performance of the optimized RISE controller in tracking task and its ability to ensure robustness with respect to bounded external disturbances