Explicit A-Priori error bounds and Adaptive error control for approximation of nonlinear initial value differential systems

This paper develops and demonstrates a guaranteed a-priori error bound for the Taylor polynomial approximation of any degree to the solution of initial value ordinary differential equations. The error bound is explicit and does not require upper bounds on the potentially complicated and intrinsically unknown right-hand side nor on any of its higher-order derivatives as with existing bounds, and thus it provides a valuable tool for the numerous applications in which initial value ode problems arise and for which approximate solutions must be sought.     

Adaptive differential quantization in digital feedback control

Adaptation of the quantizer step-size is proposed as a potentially useful means of obtaining robust performance of the feedback-signal quantizer in digital control systems which are subject to wide fluctuations in mean-square plant disturbance. Design considerations for ‘one-word memory’ step-size adaptation algorithms are discussed, and simulation results are presented for examples. These results demonstrate the robust performance of the system over a wide range of plant disturbance variance.     

Adaptive control with the stochastic approximation algorithm: Geometry and convergence

New geometric properties possessed by the sequence of parameter estimates are exhibited, which yield valuable insight into the behavior of the stochastic approximation based algorithm as it is used in minimum variance adaptive control. In particular, these geometric properties, together with certain probabilistic arguments, prove that if the system does not have a reduced-order minimum variance controller, then the parameter estimates converge to a random multiple of the true parameter. An explicit expression for the limiting parameter estimate is also available. With strictly positive probability, the limiting parameter estimate is not the true parameter, and in some cases differs from the true parameter with probability one. If the system possesses reduced-order minimum variance controllers, then convergence to a minimum variance controller in a Cesaro sense is shown. The geometry of the limit set is described. Sufficient conditions are also given for some of these results to hold for parameter estimation schemes other than stochastic approximation.     

Adaptive differential dynamic programming for multiobjective optimal control

An efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the “optimal” weighting coefficients for various performance indices are time-varying as the system evolves along any noninferior trajectory. Recognizing this prominent feature in multiobjective control, the proposed adaptive differential dynamic programming methodology combines a search process to identify an optimal time-varying weighting sequence with the solution concept in the conventional differential dynamic programming. Convergence of the proposed adaptive differential dynamic programming methodology is addressed.     

Robust explicit model predictive control via regular piecewise-affine approximation

This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. First, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforced a priori, rather than checked a posteriori via Lyapunov analysis.     

Adaptive control of nonlinear systems via approximate linearization

This paper presents an adaptive control scheme for nonlinear systems that violates some of the common regularity and structural conditions of current nonlinear adaptive schemes such as involutivity, existence of a well-defined relative degree, and minimum phase property. While the controller is designed using an approximate model with suitable properties, the parameter update law is derived from an observation error based on the exact model described in suitable coordinates. The authors show that this approach results in a stable, closed-loop system and achieves adaptive tracking with bounds on the tracking error and parameter estimates. The authors also present a constructive procedure for adaptive state regulation which is based on the quadratic linearization technique via dynamic state feedback. This regulation scheme does not impose any restriction on the location of the unknown parameters and is applicable to any linearly controllable nonlinear system     

Adaptive stabilization of linear systems via switching control

In this paper, we develop a method for adaptive stabilization without a minimum-phase assumption and without knowledge of the sign of the high-frequency gain. In contrast to recent work by Martensson [8], we include a compactness requirement on the set of possible plants and assume that an upper bound on the order of the plant is known. Under these additional hypotheses, we generate a piecewise linear time-invariant switching control law which leads to a guarantee of Lyapunov stability and an exponential rate of convergence for the state. One of the main objectives in this paper is to eliminate the possibility of "large state deviations" associated with a search Over the space of gain matrices which is required in [8].     

Adaptive control via consistent estimation for deterministic systems

For multidimensional discrete-time deterministic systems the optimal adaptive control has been derived by use of a probabilistic method so that when the reference signal is an arbitrary bounded random sequence, the tracking error and the estimation error based on a projection algorithm go to zero with a near-exponential convergence rate. For this, the basic step is to prove the consistency of estimates when the condition number of the matrix consisting of regressors diverges to infinity; in other words, when the persistent excitation condition is not satisfied.     

Adaptive control of robot manipulators via velocity estimatedfeedback

An approach for designing robot controllers using state-space feedback is presented. The robot model parameters are assumed to be unknown and velocity measurements are assumed not to be available. This asymptotically stable control scheme combines an adaptive control law with a sliding observer and does not need additional assumptions on the variation of the inertia matrix eigenvalues. State observation and parameter adaptation are performed simultaneously. The adaptation law, the observer gains, and the control law are designed on the reduced order manifold which results from the invariance of the switching surface     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

Adaptive control of parallel manipulators via fuzzy-neural network algorithm

This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms (FNNA).With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric uncertainties are eliminated. FNNA is used to handle model uncertainties and external disturbances. In the proposed control scheme, we consider modifying the weight of fuzzy rules and present these rules to a MIMO system of parallel manipulators with more than three degrees-of-freedom (DoF). The algorithm has the advantage of not requiring the inverse of the Jacobian matrix especially for the low DoF parallel manipulators. The validity of the control scheme is shown through numerical simulations of a 6-RPS parallel manipulator with three DoF.     

Adaptive control of parallel manipulators via fuzzy-neural network algorithm

This paper considers adaptive control of parallel manipulators combined with fuzzy-neural network algorithms （FNNA）. With this algorithm, the robustness is guaranteed by the adaptive control law and the parametric uncertainties are eliminated. FNNA is used to handle model uncertainties and external disturbances. In the proposed control scheme, we consider modifying the weight of fuzzy rules and present these rules to a MIMO system of parallel manipulators with more than three degrees-of-freedom （DoF）. The algorithm has the advantage of not requiring the inverse of the Jacobian matrix especially for the low DoF parallel manipulators. The validity of the control scheme is shown through numerical simulations of a 6-RPS parallel manipulator with three DoF.     

Some results in differential approximation

A numerical method for solving midly non-linear elliptic problems over irregular regions is proposed in the paper. The given irregular region is imbedded in a region of simple geometry. The original non-linear problem is replaced by a sequence of linear problems by using the technique of quasi-linearisation. The method of dynamic programming is then used for computing the required solutions. The method is illustrated by solving a given problem. It is found that the proposed method is fast and can be applied to problems over complex regions.     

Adaptive neural complementary sliding-mode control via functional-linked wavelet neural network

Chaos control can be applied in the vast areas of physics and engineering systems, but the parameters of chaotic system are inevitably perturbed by external inartificial factors and cannot be exactly known. This paper proposes an adaptive neural complementary sliding-mode control (ANCSC) system, which is composed of a neural controller and a robust compensator, for a chaotic system. The neural controller uses a functional-linked wavelet neural network (FWNN) to approximate an ideal complementary sliding-mode controller. Since the output weights of FWNN are equipped with a functional-linked type form, the FWNN offers good learning accuracy. The robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Without requiring preliminary offline learning, the parameter learning algorithm can online tune the controller parameters of the proposed ANCSC system to ensure system stable. Finally, it shows by the simulation results that favorable control performance can be achieved for a chaotic system by the proposed ANCSC scheme.     

Adaptive observer and nonlinear control strategy for chemical reactors via neural networks

An adaptive observer and nonlinear feedback control strategy with constraints on control action are developed by using a supervised learning rule of a neural network and the theory of functional-link networks. The convergence of the adaptive observer and the stability of the control system are proven. They are applied to the control of an exothermic stirred-tank reactor. It is shown that an adaptive observer for concentration can be constructed for a reaction system when only temperature measurements are available on line. An adaptive observer is used to identify the pre-exponential Arrhenius constant and to provide on line estimation of the unmeasured reactant concentration for a nonlinear state-feedback controller. Simulations show that the combined observer/controller provides satisfactory closed-loop behaviour, fast responses and strong robustness. Estimated and actual concentration are in good agreement. A nonlinear feedback controller can provide effective feedback control over a wide range of operating conditions.     

Adaptive control of pure-feedback systems with nonlinear parameterization via time-scale separation

International Journal of Control, Automation and Systems - In this paper an adaptive control approach for completely non-affine pure-feedback systems with nonlinear parameterization is proposed. By...     

Edgeworth approximation of multivariate differential entropy

We develop the general, multivariate case of the Edgeworth approximation of differential entropy and show that it can be more accurate than the nearest-neighbor method in the multivariate case and that it scales better with sample size. Furthermore, we introduce mutual information estimation as an application.