连铸方坯的二冷水控制问题

对连铸过程的二冷水控制问题进行了讨论;将二维凝固温度场的边界控制问题,用线性化方法将原问题等价地转化为在几个Ｒａｎｄｏｎ测试空间求最优测度的有限维线性优化问题,从而得到全局最优控制律。数值试验显示此方法是有效的。     

A dual maximum principle for discrete-time linear systems with economic applications

A discrete-time linear optimal control problem with given initial and terminal times, state control constraints, and variable end points is set forth. Corresponding to this primal control problem, or maximization problem, is a dual linear control problem, or minimization problem. A dual maximum principle is proved with the aid of the duality theory of linear programming, where the dual of the Hamiltonian of the primal control problem is the Hamiltonian of the dual control problem. A discrete-time analog of the Hamilton-Jacobi equation is derived; and economic applications are discussed.     

Stabilizing static output feedback receding horizon controls for linear discrete time-invariant systems

In this paper, a stabilizing static output feedback receding horizon control (RHC) is proposed for linear discrete time-invariant systems. An inequality condition on the terminal weighting matrices is presented under which the closed-loop stability of static output feedback receding horizon controls is guaranteed. It is shown that the stabilizing static output feedback receding horizon control problem can be represented as a non-linear minimization problem based on linear matrix inequalities (LMIs). An algorithm for solving the presented non-linear minimization problem is proposed. In addition, this result is extended to an arbitrary reference tracking problem that is one of the main features of receding horizon control. Finally, the efficiency of the proposed algorithm is illustrated by numerical examples.     

Matrix criterion robust linear quadratic control problem

This paper studies a robust linear quadratic (LQ) control problem with multiple quadratic performance indices. Specifically, a linear model is assumed to be available for each of a prespecified set of operating points of a system. A vector-valued quadratic control performance index is given at each operating point. It is then desired to find the constant feedback gains of a linear controller to obtain satisfactory control performance over all the operating points. This is a realistic case involving the minimization of a vector criterion of vector criteria, i.e. a matrix-valued criterion. The matrix-valued criterion gives insight into standard robust LQ design, and leads to several related vector minimization problems, and to natural procedures for computing a satisfactory non-inferior solution to the matrix-valued minimization problem.     

Decentralized stabilization of large electric power systems

This paper considers the problem of stabilizing the dynamics of a large electric power system, represented by a linear time invariant system of equations, by using several decentralized (or local) state feedback control laws. The stabilization problem is formulated into a functional minimization problem which implicitly controls the closed-loop eigenvalues of the controlled system. The constraint of decentralization is tackled in the minimization algorithm by using the method of feasible directions. To illustrate the application of the algorithm, it is used to stabilize a three machine electric power system.     

Multiple models,multiplicative noise and linear quadratic control—algorithmic aspects

Numerical solution of certain linear quadratic (LQ) control problems for robust design is addressed. An iterative method is suggested and analysed for solving a minimax multiple model LQ control problem. A convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants. Furthermore, a convergent iterative method is proposed for solving the maximum entropy parametric LQ control problem with multiplicative noise.     

Minimization of Overshoot in Linear Discrete-Time Systems via Low-Order Controllers

For the SISO linear discrete-time control systems, a technique of response optimization was proposed. It is based on introducing a performance function which is the upper bound of the maximum of error magnitude. Its minimization leads to a linear programming problem in the controller coefficients. Importantly, a low-order controller can be designed in this manner. Various generalizations of the problem, including the robust variant, were considered.     

具有异步时钟的长时延网络控制系统故障检测

考虑一类存在异步采样时钟的不确定长时延网络控制系统．假定其可能发生故障，设计了离散状态观测器，对其进行故障检测．当系统正常时，观测器系统的稳定性条件被近似为一个包含线性矩阵不等式条件的最小化问题；只要该最小化问题有解，则整个系统是渐近稳定的．当系统发生故障时，该观测器残差能够迅速发生跳变，从而检测出故障的发生．给出一个仿真示例验证了文中方法的有效性．     

Bi-criteria Velocity Minimization of Robot Manipulators Using a Linear Variational Inequalities-Based Primal-Dual Neural Network and PUMA560 Example

In this paper, to diminish discontinuity points arising in the infinity-norm velocity minimization scheme, a bi-criteria velocity minimization scheme is presented based on a new neural network solver (i.e., a primal-dual neural network based on linear variational inequalities (LVI)). Such a kinematic control scheme of redundant manipulators can incorporate joint physical limits such as joint limits and joint velocity limits simultaneously. Moreover, the presented kinematic control scheme can be formulated as a quadratic programming (QP) problem. As a real-time QP solver, the LVI-based primal-dual neural network is established with a simple piecewise linear structure and higher computational efficiency. Computer simulations performed based on a PUMA560 manipulator are presented to illustrate the validity and advantages of such a bi-criteria neural control scheme for redundant robots.     

A Simultaneous Mixed LQR/H∞ Control Approach to the Design of Reliable Active Suspension Controllers

This paper is concerned with the synthesis of reliable controllers for quarter‐car active suspension systems. By a simultaneous mixed LQR/H_∞ control approach, a static output feedback controller is derived for guaranteeing good suspension performance under possible sensor fault or suspension component breakdown. The considered simultaneous mixed LQR/H_∞ control problem is a nonconvex optimization problem; therefore, the linear matrix inequality approach is not applicable. Based on the barrier method, we solve an auxiliary minimization problem to get an approximate solution for the simultaneous mixed LQR/H_∞ control problem. Necessary conditions for the local optimum of the auxiliary minimization problem are derived. Moreover, a three‐stage solution algorithm is developed for solving the auxiliary minimization problem. The simulation shows that the obtained static output feedback suspension controllers can improve suspension performance in nominal mode and all considered failure modes.     

Reduced order H∞ control of an autonomous underwater vehicle

It is well known that the reduced-order (least-order) H_∞ control problem is a rank minimization problem subject to linear matrix inequality (LMI) constraints which is hard to solve due to the non-convexity of the objective and the trace heuristic is simple and efficient one among various heuristics that approximate the rank minimization problem. In this paper, a theoretical insight into the trade-off between the controller order and the performance of the closed-loop system is given. Autopilots (forward speed, heading and depth) for an autonomous underwater vehicle are synthesized based upon the trace heuristic. Simulation results as well as experimental results of heading control show that the reduced-order autopilots are desirable for practical implementation due to their simple structures and slight performance degradation.     

Linear adaptive control for nonstationary uncertain systems under bounded noise

A discrete-time nonstationary linear control system is considered to be given by the algebraic difference equation in the state space. The control system is subject to a bounded additive noise. Uncertain parameters of the system take their values on the given polytopes which evolve in time. The objective is to generate a linear feedback, which provides the minimization of a given performance criterion in adaptive way. In general, the control problem is reduced to the convex programming one of an insignificant computational complexity. Therewith, the control problem can be solved analytically in the case of interval set-valued parameter estimates.     

On linear programming and robust model-predictive control using impulse-responses

Campo and Morari have derived a linear programming problem, with a potentially large number of constraints, which is equivalent to a min-max formulation for robust model-predictive control of linear systems. That formulation involves minimization, with respect to the controls, of the maximum, with respect to the system's impulse response (from a set of possible impulse responses), of the infinity norm of the error between the predicted and required system output sequences. Here an alternative linear programming problem is derived which has a smaller number of constraints and is therefore potentially more convenient for on-line control.     

Identification by a combined smoothing nonlinear programming algorithm

An offline algorithm is developed for identification of parameters of linear, stationary, discrete, dynamic systems with known control inputs and subjected to process and measurement noise with known statistics. Results of the algorithm include estimates of the parameters and smoothed estimates of the state and process noise sequences. The problem is stated as the minimization of a quadratic performance index. This minimization problem is then converted to a nonlinear programming problem for determining the optimum parameter estimates. The new algorithm is shown to be cost competitive with the currently popular filtering-sensitivity function method. A third order example with simulated data is presented for comparison.     

Designing of non-fragile robust model predictive control for constrained uncertain systems and its application in process control

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.     

一类不确定模糊模型的输出反馈鲁棒预测控制

针对一类满足扇形界条件的不确定模糊模型描述的非线性系统,提出一种输出反馈鲁棒预测控制方法．该方法将鲁棒预测控制的Min-Max优化问题转化为具有LMI约束的线性目标最小化问题,并且不需系统状态完全可测,仅仅利用系统测量输出和不可测状态的界限值来确定保证闭环系统鲁棒稳定的输出反馈控制器．仿真实验证明了该方法的有效性．     

Optimal control problem in bond graph formalism

This paper presents a new way to derive an optimal control system for a specific optimisation problem, based on bond graph formalism. The procedure proposed concerns the optimal control of linear time invariant MIMO systems and can deal with both cases of the integral performance index, these correspond to dissipative energy minimization and output error minimization. An augmented bond graph model is obtained starting from the bond graph model of the system associated with the optimal control problem. This augmented bond graph, consisting of the original model representation coupled to an optimizing bond graph, supplies, by its bicausal exploitation, the set of differential-algebraic equations that analytically give the solution to the optimal control problem without the need to develop the analytical steps of Pontryagin’s method. The proof uses the Pontryagin Maximum Principle applied to the port-Hamiltonian formulation of the system.