Shuzhi Sam Ge

Stable Adaptive Neural Network Control

While neural network control has been successfully applied in various practical applications, many important issues, such as stability, robustness, and performance, have not been extensively researched for neural adaptive systems. Motivated by the need for systematic neural control strategies for nonlinear systems, Stable Adaptive Neural Network Control offers an in-depth study of stable adaptive control designs using approximation-based techniques, and presents rigorous analysis for system stability and control performance. Both linearly parameterized and multi-layer neural networks (NN) are discussed and employed in the design of adaptive NN control systems for completeness. Stable adaptive NN control has been thoroughly investigated for several classes of nonlinear systems, including nonlinear systems in Brunovsky form, nonlinear systems in strict-feedback and pure-feedback forms, nonaffine nonlinear systems, and a class of MIMO nonlinear systems. In addition, the developed design methodologies are not only applied to typical example systems, but also to real application-oriented systems, such as the variable length pendulum system, the underactuated inverted pendulum system and nonaffine nonlinear chemical processes (CSTR).

Analysis and synthesis of switched linear control systems

Switched linear systems have a long history of interest in the control community, and have attracted considerable attention recently because they are not only practically relevant, but also tangible with the rich results in the linear system theory. Rapid progress in the field has generated many new ideas and powerful tools. This paper provides a concise and timely survey on analysis and synthesis of switched linear control systems, and presents the basic concepts and main properties of switched linear systems in a systematic manner. The fundamental topics include (i) controllability and observability, (ii) system structural decomposition, (iii) feedback controller design for stabilization, and (iv) optimal control.

New potential functions for mobile robot path planning

The paper first describes the problem of goals unreachable with obstacles nearby when using potential field methods for mobile robot path planning. Then, new repulsive potential functions are presented by taking the relative distance between the robot and the goal into consideration, which ensures that the goal position is the global minimum of the total potential.

Adaptive neural control of uncertain MIMO nonlinear systems

In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.

Dynamic Motion Planning for Mobile Robots Using Potential Field Method

The potential field method is widely used for autonomous mobile robot path planning due to its elegant mathematical analysis and simplicity. However, most researches have been focused on solving the motion planning problem in a stationary environment where both targets and obstacles are stationary. This paper proposes a new potential field method for motion planning of mobile robots in a dynamic environment where the target and the obstacles are moving. Firstly, the new potential function and the corresponding virtual force are defined. Then, the problem of local minima is discussed. Finally, extensive computer simulations and hardware experiments are carried out to demonstrate the effectiveness of the dynamic motion planning schemes based on the new potential field method.

Barrier Lyapunov Functions for the control of output-constrained nonlinear systems

In this paper, we present control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint. To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we ensure that those limits are not transgressed. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output. Furthermore, we explore the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. We also compare our control with one that is based on a Quadratic Lyapunov Function, and we show that our control requires less restrictive initial conditions. A numerical example is provided to illustrate the performance of the proposed control.

Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semi-global uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

Brief paper: Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form

In this paper, adaptive dynamic surface control (DSC) is developed for a class of pure-feedback nonlinear systems with unknown dead zone and perturbed uncertainties using neural networks. The explosion of complexity in traditional backstepping design is avoided by utilizing dynamic surface control and introducing integral-type Lyapunov function. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system, with arbitrary small tracking error by appropriately choosing design constants. Simulation results demonstrate the effectiveness of the proposed approach.

Robust Adaptive Neural Network Control for a Class of Uncertain MIMO Nonlinear Systems With Input Nonlinearities

In this paper, robust adaptive neural network (NN) control is investigated for a general class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with unknown control coefficient matrices and input nonlinearities. For nonsymmetric input nonlinearities of saturation and deadzone, variable structure control (VSC) in combination with backstepping and Lyapunov synthesis is proposed for adaptive NN control design with guaranteed stability. In the proposed adaptive NN control, the usual assumption on nonsingularity of NN approximation for unknown control coefficient matrices and boundary assumption between NN approximation error and control input have been eliminated. Command filters are presented to implement physical constraints on the virtual control laws, then the tedious analytic computations of time derivatives of virtual control laws are canceled. It is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed-loop system. Finally, simulation results are presented to illustrate the effectiveness of the proposed adaptive NN control.

Direct adaptive NN control of a class of nonlinear systems

In this paper, direct adaptive neural-network (NN) control is presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By utilizing a special property of the affine term, the developed scheme,avoids the controller singularity problem completely. All the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.