Design of optimal trajectory transition controller for thrust-vectored V/STOL aircraft

Dear editor, In recent years, vertical and/or short take-off and landing (V/STOL) aircraft have attracted much attention because they combine the efficiency of ...     

Control allocation for a V/STOL aircraft based on robust fuzzy control

This study addresses the design of an output-feedback H-infinity and fuzzy mixed controller for an advanced vertical and/or short take-off and landing aircraft that exhibits satisfactory global stability criteria. A fuzzy logic based optimization approach is employed to solve autonomously the constrained control allocation problem by suitably adjusting the components of the output vector and finding a proper vector in the attainable moment set. Simulations show that the designed fuzzy controller is better s...     

Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.     

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.     

Optimal control laws for a class of constrained linear-quadratic problems

In general it seems impossible to specify the form of the solution of the linear-quadratic optimal control problem when there are control constraints. This paper deals with a restricted class of quadratic performance criteria, for which the optimal feedback control law is shown to be linear-in-half-spaces when the control is constrained to take values in a closed cone $\text{Γ ?}\text{R}{}^{\mathrm{<mtext>m</mtext>}}$. The time-varying vector quantities which are required for implementation of the optimal control law may be pre-computed by solving two initial-value problems for certain nonlinear first-order ordinary differential equations, and maximizing a quadratic function over the cone Γ at each time. The instants at which the solutions of these initial-value problems blow up are precisely the ‘escape times’ at which the performance criterion becomes unbounded below on some half-space. Analogues of the familiar Riccati equation are also presented.     

H Optimal control for linear stochastic systems

The aim of the present paper is to provide an optimal solution to the H² state-feedback and output-feedback control problems for stochastic linear systems subjected both to Markov jumps and to multiplicative white noise. It is proved that in the state-feedback case the optimal solution is a static gain which is also optimal in the class of all higher-order controllers. In the output-feedback case the optimal H² controller has the same order as the given stochastic system. The realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of Riccati-type coupled equations. An effective iterative convergent algorithm to compute these stabilizing solutions is also presented. The paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature.     

一类受约束非线性系统的有限时间优化镇定

优化控制方法可以考虑系统性能和节省能源,但是不能给出初始稳定区域的描述.本文阐述的优化控制方法可以给出初始稳定区域的描述,使得约束非线性系统有限时间稳定.首先设计有限时间优化控制器使得系统的状态在有限时间内进入初始稳定区域,同时优化目标函数,系统实现性能最优和消耗最小.进而设计有限时间鲁棒镇定控制器使得系统的状态在有限时间内收敛到原点. Lyapunov函数分析方法给出了吸引域的估计,并确保在不同状态下,设计的控制器使得闭环系统有限时间稳定.最后给出了一个仿真实例验证算法的有效性.     

Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile.     

一类具有数据包丢失的网络控制系统的最优控制

针对控制器和执行器均采用时钟驱动且最大丢包率和最大连续丢包长度被限定的短时延网络控制系统,提出一种数据包丢失的估值补偿方法.该方法可以根据历史状态向量和控制向量信息估算出当前的控制量.利用该方法和动态规划算法,导出了离散二次型性能指标下的网络控制系统的最优控制序列,进而给出最优控制律的实现算法.数值仿真算例验证了所得结果的有效性和正确性.     

Optimal tracking control for nonlinear large-scale systems with persistent disturbances

This paper studies the optimal control with zero steady-state error problem for nonlinear large-scale systems affected by external persistent disturbances. The nonlinear large-scale system is transformed into N nonlinear subsystems with interconnect terms. Based on the internal model principle, a disturbance compensator is constructed such that the ith subsystem with external persistent disturbances is transformed into an augmented subsystem without disturbances. According to the sensitivity approach, the optimal tracking control law for the ith nonlinear subsystem can be obtained. The optimal tracking control law for the nonlinear large-scale systems can be obtained. A numerical simulation shows that the method is effective.     

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.     

Singular H∞ Suboptimal Control for a Class of Nonlinear Cascade Systems

In the present paper singular state feedback _∞ suboptimal control for a class of nonlinear cascade systems is addressed. Under the assumption that a regular state feedback _∞ suboptimal control problem is solvable for a particular subsystem of the cascade system, an auxiliary nonlinear system is defined. It is shown that a state feedback solution to the singular _∞ suboptimal control problem for the auxiliary system also applies to the original problem. The advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable. It is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input-output decoupled. The theory is applied to a problem of a rigid spacecraft with actuator dynamics. Application to the special case when a subsystem of the nonlinear cascade system is passive is also considered.     

Optimal solutions to a class of power management problems in mobile robots

This paper studies an approach to minimize the power consumption of a mobile robot by controlling its traveling speed and the frequency of its on-board processor simultaneously. The problem is formulated as a discrete-time optimal control problem with a random terminal time and probabilistic state constraints. A general solution procedure suitable for arbitrary power functions of the motor and the processor is proposed. Furthermore, for a class of realistic power functions, the optimal solution is derived analytically. Interpretations of the optimal solution in the practical context are also discussed. Simulation results show that the proposed method can save a significant amount of energy compared with some heuristic schemes.     

On the Lyapunov-based adaptive control redesign for a class of nonlinear sampled-data systems

Stabilization of the exact discrete-time models of a class of nonlinear sampled-data systems, with an unknown parameter, is addressed. Given a Lyapunov-based continuous-time adaptive controller that ensures some stability properties for the closed-loop system, a sufficient condition for the design of high order discrete-time controllers is given. The stability analysis is carried out considering the truncated Fliess series of the Lyapunov difference equation. Due to the appearance of power terms of the unknown parameter, the problem is reparameterized in a convex-like form and an estimation law for the new unknown parameter is derived with no need of overparametrization or projection techniques. Then, assuming appropriate conditions hold, high order controllers can be designed. The boundedness of the extended state vector is ensured under some conditions, for a sufficiently small sampling period. It is shown how increasing the controller order can improve system performance.     

ISE-optimal nonminimum-phase compensation for nonlinear processes

This work concerns the optimal regulation of single-input–single-output nonminimum-phase nonlinear processes. The problem of calculation of an ISE-optimal, statically equivalent, minimum-phase output for nonminimum-phase compensation is formulated using Hamilton–Jacobi theory and the normal form representation of the nonlinear system. A Newton–Kantorovich iteration is developed for the solution of the pertinent Hamilton–Jacobi equations, which involves solving a Zubov equation at each step of the iteration. The method is applied to the problem of controlling a nonisothermal CSTR with Van de Vusse kinetics, which exhibits nonminimum-phase behaviour.     

Suboptimal control for nonlinear systems: a successive approximation approach

This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear systems with a quadratic performance index. By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation examples are employed to test the validity of the SAA.     

Optimal therapy scheduling for a simplified HIV infection model

This work is motivated by the drug therapy scheduling problem in HIV infection. Using simplified switched linear system models of HIV mutation and treatment with certain class of symmetry and finite horizon cost functions, we demonstrate that the optimal state and costate trajectories lie on a sliding surface where infinitely fast switching may occur. Results suggest that in the absence of other practical constraints, switching rapidly between therapies is relevant. Simulations show the potential benefits of a proactive switching strategy to minimize viral load and delay the emergence of resistant mutant viruses.     

Affine and predictive control policies for a class of nonlinear systems

The input-state linear horizon (ISLH) for a nonlinear discrete-time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable. In this paper, we employ the latter concept and show that the class of constraint admissible N-step affine state-feedback policies is equivalent to the associated class of constraint admissible disturbance-feedback policies, provided that N is less than the system’s ISLH. The result generalizes a recent result in [Goulart, P. J., Kerrigan, E. C., Maciejowski, J. M. (2006). Optimization over state feedback policies for robust control with constraints. Automatica, 42(4), 523-533] and is significant because it enables one: (i) to determine a constraint admissible state-feedback policy by employing well-known convex optimization techniques; and (ii) to guarantee robust recursive feasibility of a class of model predictive control (MPC) policies by imposing a suitable terminal constraint. In particular, we propose an input-to-state stabilizing MPC policy for a class of nonlinear systems with bounded disturbance inputs and mixed polytopic constraints on the state and the control input. At each time step, the proposed MPC policy requires the solution of a single convex quadratic programme parameterized by the current system state.     

带有持续扰动的时滞非线性大系统的最优跟踪控制

研究具有外界持续扰动的时滞非线性大系统的无静差最优跟踪控制问题.将时滞非线性大系统分解为带有互联项的N个时滞非线性子系统,基于内模原理对子系统构造扰动补偿器,将带有外部持续扰动的子系统化为无扰动的增广系统.通过灵敏度法求解不含时滞的两点边值问题,得到子系统的最优跟踪控制律,截取最优跟踪控制律的前N项作为次优控制律来近似系统的最优控制律.仿真实例表明了该设计方法的有效性.     

Leader-following consensus for a class of second-order nonlinear multi-agent systems

This paper deals with the leader-following consensus problem for a class of multi-agent systems with nonlinear dynamics and directed communication topology. The control input of the leader agent is assumed to be unknown to all follower agents. A distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents, which achieves leader-following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent. Compared with previous results, the nonlinear functions are not required to satisfy the globally Lipschitz or Lipschitz-like condition and the adaptive consensus protocol is in a distributed fashion. A numerical example is given to verify our proposed protocol.