An optimal control problem with piecewise quadratic cost functional containing a ‘dead-zone’

In this paper, we describe an exact solution method for the problem of optimally controlling a deterministic discrete linear system with piecewise quadratic cost functional containing a ‘dead-zone’. This model generalizes the well-known optimal control model for a linear system with (symmetric) quadratic objective functional. This more general problem is solved by using concepts and techniques from the theory of nonlinear programming, for example Kuhn-Tucker theory, duality, linear complementarity, and Lemke's algorithm. We apply the results to the solution of a 25-period deterministic pension funding problem which is modelled as a discrete-time optimal control problem. The controls for this problem are company contributions and investment amounts, and the state is the value of the pension fund.     

Optimal maintenance of a system of machines with weakest-link-dependent performance

This paper considers the maintenance policy of a system of machines whose deterioration is dependent on the machines' quality states and maintenance efforts. The return of the system of machines, however, is dependent only on the machine with the lowest quality state. This becomes a realistic feature when the machines are arranged in series as part of an assembly line production. This feature also gives rise to an unconventional optimization problem with an interesting theoretical challenge. The problem is subsequently formulated as a constrained optimal control problem. It is first shown that the problem admits an optimal control. Then, by using the control parametrization approach, an efficient computational scheme is devised for solving the problem.     

Well-posedness of a model order reduction for singularly perturbed linear stochastic systems

An order reduction problem for the state estimation of singularly perturbed linear systems is shown to be a well-posed problem, whereas the corresponding order reduction control problem is ill-posed. This observation plays an important role in the concept of multimodeling and in the slow—fast decomposition control problem for singularly perturbed linear stochastic systems.     

Minimum horizontal rotations

The problem treated here is to rotate a rigid body from one arbitrary angular orientation to another using only rotations about horizontal axes. The total rotation angle is to be minimized. This problem is formulated and solved as an optimal control problem. The solution is both simple and elegant. Examples are provided to illustrate the results. The problem is motivated by the desire to use the Earth's magnetic field for satellite attitude control.     

A discrete filled function method for the optimal control of switched systems in discrete time

In this paper, we consider the optimal control problem of discrete‐time switched systems. This problem is formulated as an optimization problem involving both continuous and discrete‐valued variables. It can be transformed into a discrete optimization problem. A metric in the space of switching sequences is introduced and an appropriate discrete filled function is constructed. Then, an algorithm that combines the discrete filled function method and a descent method is developed for solving this problem. For illustration, some numerical examples are solved. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal control of production and marketing systems with distributed time lags

This paper deals with the problem of production and advertising policy for a decaying item whose gradual loss of potential or utility is associated with the passage of time, such as grain, photographic film or electronic components. The delay effects of the advertisement on the sales rate are also considered in the problem. This leads to a control problem where the state equations are represented by integro-differential equations. The objective is to use optimal control theory to determine the production and advertising rates of the decay item which maximize the current value of net profit stream. For the model developed we present a computational procedure of finding the optimal policy and then carry out sensitivity analysis through an example problem. The properties of the optimal solution are discussed for the case of constant rate of delay effect.     

Towards global solutions of optimal discrete‐valued control problems

This paper proposes a new heuristic approach for solving optimal discrete‐valued control problems. We illustrate the approach with an existing hybrid power system model. The problem of choosing an operating schedule to minimize generator, battery, and switching costs is first posed as a mixed discrete dynamic optimization problem. Then, a discrete filled function method is employed in conjunction with a computational optimal control technique to solve this problem. Computational results indicate that this approach is robust, efficient, and can successfully identify a near‐global solution for this complex applied optimization problem despite the presence of multiple local optima. Copyright © 2011 John Wiley & Sons, Ltd.     

Gauzoma Mimicking Siliconoma After Breast Augmentation Surgery

Gauzoma is a rare iatrogenic mass caused by the retention of gauze fibers during surgery. This intraoperative complication represents a diagnostic problem for radiologists besides being a medicolegal problem for surgeons. We present a patient in whom a retained surgical sponge after breast augmentation surgery mimicked a siliconoma and discuss imaging appearance and differential diagnosis.     

Mixed H2/H∞ robust output feedback sliding mode control

This paper presents an output feedback sliding mode control scheme for uncertain dynamical systems. The design problem is solved in two steps, involving first a state feedback and then an output feedback problem. First, using the null space dynamics, the sliding surface for the unmatched uncertainty is designed. Then, by tuning the sliding surface, a robust controller is constructed for the whole uncertainty; this problem takes the form of static‐output feedback. Based on this, a dynamic output feedback controller for the system augmented with the sliding surface is designed. The synthesis involves the solution of an Linear Matrix Inequality (LMI) and Bilinear Matrix Inequality (BMI) problem; the BMI problem is solved iteratively. The proposed approach is illustrated by applying it to a well‐known robust benchmark problem and also experimentally on a spring mass system with variable stiffness. Simulation and experimental results show that the proposed method outperforms previous approaches in terms of robust performance. Copyright © 2011 John Wiley & Sons, Ltd.     

An algorithm for optimal scheduling of a class of cascade water supply systems

The problem of determining overall optimized control schedules for a class of cascade water supply systems containing only fixed speed pumps is examined. The system control is by nature an on-off type. The optimal scheduling problem can be formulated as dynamical optimal control problems with purely discrete symbols, discrete controls and also with continuous intermediate variables interrelated in a highly non-linear way. An efficient problem solver is proposed. Its high efficiency is achieved by exploiting, through a suitable decomposition, certain structural properties of the problem. Lagrange relaxation is applied in order to break down the time structure of discrete control variables. The decomposition also enables consideration of mixed integer optimization on purely static grounds. The dynamical optimization constitutes only that part of the solver which deals with entirely continuous variables. There is a duality gap in the problem. However, certain, but not complete, information obtained through solving the dual problem (dual optimal information) is close to that which corresponds to the true (primal) optimal solution. This is an important property of the scheduling problem, which together with the problem structure creates a basis for the solver design.     

A time-optimal drug displacement problem

The interaction between the two drugs, warfarin and phenylbutazone, is considered through a previously derived model. A minimum time problem, which involves a state constraint is formulated. This problem is investigated both analytically and numerically. The numerical results are obtained by transforming the state constrained problem to one which is singular and then using a conjugate gradient algorithm to obtain approximations to the optimal control. Further approximations to the control, the rate of infusion of phenylbutazone, are made so that the time profile is feasible for practical implementation.     

Optimization and control of a fedbatch fermentation process

This paper describes the optimization problem of a fedbatch fermentation process for alcohol production which initially consists of minimizing a time-optimal global criterion. Dynamic programming methods have previously allowed one to solve this global optimization problem and to deduce a local criterion to be maximized at each sampling step by using non-linear programming techniques. It is then stated that under a few realistic constraints the optimization problem can be translated into the regulation problem of the substrate concentration in the fermentor. The optimal value is a function of a certain growth model. A control law based on the quotient between measurement and optimal value is then implemented. Simulation results and real-life experiments validate the problem transformation.     

The solution of finite-time optimal control problems with control time delays

The design of deterministic LQP optimal control systems is considered for plants with control delays and a finite optimization interval. First, a solution is obtained to the fixed end-point optimal control problem. An expression for the open-loop optimal control is derived in the s-domain. The closed-loop optimal time-varying gain matrix is then calculated from the s-domain results. The open-loop and closed-loop solutions to the free end-point optimal control problem are also given. The constant gain, infinite-time, feedback control law is obtained as a limiting case of these results. The receding-horizon optimal control problem for plants with control signal delays is also considered. The solution to this problem yields a constant feedback gain matrix which has obvious advantages for implementation. This gain matrix is not the same as the constant solution to the infinite-time problem. The receding-horizon control laws are derived for both the fixed and free end-point problems, and these are shown to produce asymptotically stable closed-loop systems.     

腹腔镜肝切除研究进展

开腹肝切除一直是肝脏良恶性病变的有效治疗方式.但开腹肝切除手术创伤大,术后并发症多.如何降低肝脏手术创伤也是摆在肝脏外科医师面前的一道难题.腹腔镜技术的兴起为肝脏外科医师提供了一条途径.但腹腔镜肝切除技术尚未成熟,本文就有关腹腔镜肝切除的相关情况进行综述.     

Joint state and parameter estimation for a nuclear reactor with fast and slow modes

The knowledge of the process state variables and coefficients is of substantial importance in many practical domains such as process control and fault detection and diagnosis. In practice, one encounters systems composed of both static and dynamic models owing to the natural difference in time response of various process variables. This paper presents an estimation algorithm for a system described by the coupled steady state and dynamic models via formulating the joint state and parameter estimation problem as a state estimation problem and using a filter for non-linear systems. In the algorithm the error covariance matrix prior to the current measurements is updated using the filtered estimates rather than the predicted quantities, having a basal impact on the convergence behaviour. The other important aspect considered is the inclusion of the unmeasured disturbances in the parameter vector. This concept has an important implication for improving the on-line detection and diagnosis of potential plant operational problems. A sodium-cooled nuclear reactor is the application problem illustrating the effectiveness of the proposed scheme.     

Guaranteed cost control for switched LPV systems via parameter and state‐dependent switching with dwell time and its application

This paper is concerned with the problem of guaranteed cost control for switched linear parameter‐varying (LPV) systems. A parameter and state‐dependent switching law with dwell time is designed. The guaranteed cost control problem for switched LPV systems is still solvable even though this problem for each subsystem is unsolvable. First, a sufficient condition ensuring the solvability of the guaranteed cost control problem for switched LPV systems is presented via multiple parameter‐dependent Lyapunov functions. Then, the parameter‐dependent controller is designed, such that the closed‐loop system is asymptotically stable with the guaranteed cost index. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an aero‐engine. Copyright © 2016 John Wiley & Sons, Ltd.     

Multi‐input control design for a constrained bilinear biquadratic regulator with external excitation

This study addresses an optimal control problem that is defined for a type of bilinear excited plant, multiple control inputs, a biquadratic finite horizon performance index, and control trajectory constraints. A novel sequence of improving functions, which suits this problem, is derived, and the corresponding Krotov's algorithm is formulated. The significance of the results is illustrated by a structural control design for a structure that is subjected to a harmonic ground acceleration input and semi‐active control constraints.     

Optimal control of linearly constrained linear systems via state parametrization

This paper presents a general computational tool for determining the near-optimal trajectories of linear, lumped parameter, dynamic systems subjected to linear constraints. In the proposed approach each state variable is approximated by the sum of a third-order polynomial and a finite term Fourier-type series. This enables a linearly constrained optimal control problem to be converted into a linearly constrained mathematical programming problem. Simulation results demonstrate that the approach accurately predicts the optimal performance index and the optimal state and control trajectories.     

Minimal time crisis versus minimum time to reach a viability kernel: A case study in the prey‐predator model

In this work, we provide a reformulation of the minimal time crisis problem associated with a constraint set as a free terminal time control problem. The proof requires the existence of a nonempty viability kernel that is reachable from the state space. In addition, we suppose a uniform lower bound between two consecutive crossing times of the constraint set. Thanks to this result, we compute an optimal synthesis for the minimal time crisis problem governed by the prey‐predator dynamics, with a controlled mortality on the predators. Finally, we compare the time spent in the crisis set by optimal trajectories of the minimal time crisis problem with the minimum time problem to reach the viability kernel. This is made possible by means of an exact characterization of the viability kernel.