Risk-sensitive control for a class of nonlinear systems with multiplicative noise

In this paper, we consider the problem of optimal control for a class of nonlinear stochastic systems with multiplicative noise. The nonlinearity consists of quadratic terms in the state and control variables. The optimality criteria are of a risk-sensitive and generalised risk-sensitive type. The optimal control is found in an explicit closed-form by the completion of squares and the change of measure methods. As applications, we outline two special cases of our results. We show that a subset of the class of models which we consider leads to a generalised quadratic–affine term structure model (QATSM) for interest rates. We also demonstrate how our results lead to generalisation of exponential utility as a criterion in optimal investment.     

严格反馈Markov 跳跃非线性系统风险灵敏度设计

在无限时区风险灵敏度指标下,研究了一类具有严格反馈形式的 Markov 跳跃非线性系统的控制器设计问题.首先,将此问题的可解性转化为一类 HJB 方程的可解性;然后根据此方程,构造性地给出一个与模态无关的控制器,此控制器可保证闭环系统是依概率有界的,且风险灵敏度指标不大于任意给定的正常数,特别地,当噪声项在原点处消逝时,能够确保风险灵敏度指标为零;最后,通过仿真例子验证了理论结果的正确性.     

Automated synthesis of control for nonlinear dynamic systems

Artificial intelligence methods appear to be particularly well suited for control design when only inexact prior knowledge about the system to be controlled is available. Design tasks that can be solved include learning control from scratch, improving partial control knowledge, and controller tuning. The paper enlightens these approaches in two case studies, both dealing with nonlinear unstable systems: inverted pendulum control, and position control of a floating object. Comparison to the classical model-based control design approaches is also provided.     

改进的非线性鲁棒自适应动态面控制

针对不确定多输入多输出严格反馈块控非线性系统,提出一种鲁棒自适应动态面控制方法.该方法在反推自适应神经网络控制中引入动态面控制简化控制律,同时对自适应律进行改进以改善系统的过渡过程动态品质,保证了系统在简化的控制律下仍具有良好的动态特性.通过Lyapunov方法证明了闭环系统所有信号均有界,系统的跟踪误差指数收敛到有界紧集内.最后给出的某新型战斗机六自由度仿真结果表明了该方法的有效性.     

Direct adaptive control of partially known nonlinear systems.

A direct adaptive control strategy for a class of single-input/single-output nonlinear systems is presented. The major advantage of the proposed method is that a detailed dynamic nonlinear model is not required for controller design. The only information required about the plant is measurements of the state variables, the relative degree, and the sign of a Lie derivative which appears in the associated input-output linearizing control law. Unknown controller functions are approximated using locally supported radial basis functions that are introduced only in regions of the state space where the closed-loop system actually evolves. Lyapunov stability analysis is used to derive parameter update laws which ensure (under certain assumptions) the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model. The technique is successfully applied to a nonlinear biochemical reactor model.     

Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Neural-network predictive control for nonlinear dynamic systems with time-delay

A new recurrent neural-network predictive feedback control structure for a class of uncertain nonlinear dynamic time-delay systems in canonical form is developed and analyzed. The dynamic system has constant input and feedback time delays due to a communications channel. The proposed control structure consists of a linearized subsystem local to the controlled plant and a remote predictive controller located at the master command station. In the local linearized subsystem, a recurrent neural network with on-line weight tuning algorithm is employed to approximate the dynamics of the time-delay-free nonlinear plant. No linearity in the unknown parameters is required. No preliminary off-line weight learning is needed. The remote controller is a modified Smith predictor that provides prediction and maintains the desired tracking performance; an extra robustifying term is needed to guarantee stability. Rigorous stability proofs are given using Lyapunov analysis. The result is an adaptive neural net compensation scheme for unknown nonlinear systems with time delays. A simulation example is provided to demonstrate the effectiveness of the proposed control strategy.     

非线性系统近似最优PD动态补偿控制

本文研究了一类基于动态补偿的非线性系统的近似最优PD控制的问题.用微分方程的逐次逼近理论将非线性系统的最优控制问题转化为求解线性非齐次两点边值序列问题,并提供了从时域最优状态反馈到频域最优PD控制器参数的优化方法,从而获取系统最优的动态补偿网络,设计出最优PD整定参数,给出其实现算法.最后仿真示例将所提出的方法与传统的线性二次型调节器（LQR）逐次逼近方法相比较,表明该方法具有良好的动态性能和鲁棒性.     

非线性系统有限时间自适应动态面容错控制

针对具有传感器故障的一类严格反馈非线性系统, 提出一种有限时间自适应动态面容错控制策略. 考虑的 传感器故障包括: 固定偏差故障、漂移故障、精度下降及失效故障. 以反步法为主要设计依据, 利用模糊逻辑系统处 理模型中的未知函数. 该控制策略的显著优势在于结合有限时间理论、容错控制、模糊逻辑控制及动态面控制, 使 得系统无论发生故障与否, 均使得系统在原点处是半全局实际有限时间稳定, 同时保证系统的实际输出信号在有限 时间内跟踪期望信号, 且跟踪误差收敛于坐标原点的小邻域内. 另外, 通过采用动态面控制技术克服了传统反步法 中的计算复杂问题. 最后, 仿真算例证明了该设计方案的有效性.     

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.     

A discrete-time multivariable neuro-adaptive control for nonlinear unknown dynamic systems

First, we assume that the controlled systems contain a nonlinear matrix gain before a linear discrete-time multivariable dynamic system. Then, a forward control based on a nominal system is employed to cancel the system nonlinear matrix gain and track the desired trajectory. A novel recurrent-neural-network (RNN) with a compensation of upper bound of its residue is applied to model the remained uncertainties in a compact subset /spl Omega/. The linearly parameterized connection weight for the function approximation error of the proposed network is also derived. An e-modification updating law with projection for weight matrix is employed to guarantee its boundedness and the stability of network without the requirement of persistent excitation. Then a discrete-time multivariable neuro-adaptive variable structure control is designed to improve the system performances. The semi-global (i.e., for a compact subset /spl Omega/) stability of the overall system is then verified by the Lyapunov stability theory. Finally, simulations are given to demonstrate the usefulness of the proposed controller.     

基于神经网络的非仿射块控非线性系统动态反演控制

即使已知非仿射非线性系统的逆存在,利用隐函数定理求解该显式逆仍然非常困难.为此,针对一类不确定块控非仿射系统,将动态反馈、反演、神经网络和反馈线性化技术相结合,提出一种自适应鲁棒控制器的设计方法.利用神经网络来逼近和消除未知函数,并证明了整个闭环系统在李雅普诺夫意义下是稳定的.仿真结果表明了所提出方法的有效性.     

Adaptive dynamic surface control for disturbance attenuation of nonlinear systems

This paper proposes an adaptive dynamic surface control (DSC) approach for disturbance attenuation of uncertain nonlinear systems in the parametric strict-feedback form. In the proposed control system, a smooth projection algorithm is employed to train uncertain parameters. The proposed DSC system can overcome the complexity of an actual controller caused by the recursive differentiation of virtual controllers and parameter adaptation laws in the backstepping design procedure. From Lyapunov stability analysis, it is shown that the proposed controller has H_∞ tracking performance to attenuate external disturbances     

基于动态非线性逼近的非线性系统预测控制

对于一类常见多重时滞非线性离散系统．提出基于动态非线性逼近的增量型最小化递推预测模型、广义预测控制律、噪声估计器以及参数自适应递推预报算法。实现了对存在较大滞后的时滞非线性系统的广义预测控制．仿真结果表明了该算法的正确性和有效性．     

Observer-based backstepping dynamic surface control for stochastic nonlinear strict-feedback systems

An observer-based dynamic surface control approach is proposed for a class of stochastic nonlinear strict-feedback systems in order to solve the problem of ‘explosion of complexity’ in the backstepping design; that is, the dynamic surface control approach is extended to the stochastic setting. The circle criterion is applied to designing a nonlinear observer, and so no linear growth condition is imposed on nonlinear functions depending on system states. It is proved that the closed-loop system is semi-globally uniformly ultimately bounded in fourth moment, and the ultimate boundedness can be tuned arbitrarily small. Two examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.     

An adaptive neuro-fuzzy tracking control for multi-input nonlinear dynamic systems

An adaptive neuro-fuzzy control design is suggested in this paper, for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities. The plant is described by a Takagi–Sugeno (T–S) fuzzy model, where the local submodels are realized through nonlinear dynamical input–output mappings. Our approach relies upon the effective approximation of certain terms that involve the derivative of the Lyapunov function and the unknown system nonlinearities. The above task is achieved locally, using linear in the weights neural networks. A novel resetting scheme is proposed that assures validity of the control input. Stability analysis provides the control law and the adaptation rules for the network weights, assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed-loop configuration. Illustrative simulations highlight the approach.     

Adaptive dynamic surface-based differential games for a class of pure-feedback nonlinear systems with output constraints

ABSTRACT

This paper investigates the zero-sum differential game problem for a class of uncertain nonlinear pure-feedback systems with output constraints and unknown external disturbances. A barrier Lyapunov function is introduced to tackle the output constraints. By constructing an affine variable at each dynamic surface control design step rather than utilising the mean-value theorem, the tracking control problem for pure-feedback systems can be transformed into an equivalent zero-sum differential game problem for affine systems. Then, the solution of associated Hamilton–Jacobi–Isaacs equation can be obtained online by using the adaptive dynamic programming technique. Finally, the whole control scheme that is composed of a feedforward dynamic surface controller and a feedback differential game control strategy guarantees the stability of the closed-loop system, and the tracking error is remained in a bounded compact set. The simulation results demonstrate the effectiveness of the proposed control scheme.     

Risk-sensitive dual control

In this paper, we develop new results concerning the risk-sensitive dual control problem for output feedback nonlinear systems, with unknown time-varying parameters. These results are not merely immediate specializations of known risk-sensitive control theory for nonlinear systems, but rather, are new formulations which are of interest in their own right. A dynamic programming equation solution is given to an optimal risk-sensitive dual control problem penalizing outputs, rather than the states, for a reasonably general class of nonlinear signal models. This equation, in contrast to earlier formulations in the literature, clearly shows the dual aspects of the risk-sensitive controller regarding control and estimation. The computational task to solve this equation, as has been seen for the risk-neutral dual control problem, suffers from the so-called ‘curse of dimensionality’. This motivates our study of the risk-sensitive version for a suboptimal risk-sensitive dual controller. Explicit controllers are derived for a minimum phase single-input, single-output auto-regressive model with exogenous input and unknown time-varying parameters. Also, simulation studies are carried out for an integrator with a time-varying gain. They show that the risk-sensitive suboptimal dual controller is more robust to uncertain noise environments compared with its risk-neutral counterpart. © 1997 by John Wiley & Sons, Ltd.     

Evolutionary asymmetric games for modeling systems of partially cooperative agents

Based on the tenet of Darwinism, we propose a general mechanism that guides agents (which can be partially cooperative) in selecting appropriate strategies in situations of complex interactions, in which agents do not have complete information about other agents. In the mechanism, each participating agent generates many instances of itself to help it find an appropriate strategy. The generated instances adopt alternative strategies from the agent's strategy set. While all instances generated by different agents meet randomly to complete a task, every instance adapts its strategy according to the difference between the average utilities of its current strategy and all its strategies. We give a complete analysis of the mechanism for the case with two agents when each agent has two strategies, and show that by the tenet of Darwinism, agents can find their appropriate strategies through evolution and adaptation: 1) if dominant strategies exist, then the proposed mechanism is guaranteed to find them; 2) if there are two or more strict Nash equilibrium strategies, the proposed mechanism is guaranteed to find them by using different initial strategy distributions; and 3) if there is no dominant strategy and no strict Nash equilibrium, then agents will oscillate periodically. Nevertheless, the mechanism allows agent designers to derive the appropriate strategies from the oscillation by integration. For cases with two agents when each agent has two or more strategies, it is shown that agents can reach a steady state where social welfare is optimum.     

一类非线性时滞系统的自适应动态面控制

本文对于一类含不确定输入时滞和干扰的非线性系统的跟踪控制问题提出了一种自适应动态面控制方案. 利用动态面控制方法避免了传统的后推设计中存在的复杂度爆炸问题. 分别构造了一个滤波器和一个虚拟观测器来产生辅助信号. 采用神经网络来逼近未知的连续函数. 跟踪误差被证明最终收敛到一个足够小的紧集. 给出了一个数字仿真示例验证了理论结果.