A stochastic optimal feedback control problem with random-sized jumps

An optimal feedback control problem for a partially observed linear system with noise of fixed-sized jumps occurring at random times driven by a Poisson process is extended to include noise with random-sized jumps. The control structure is appropriately modified to compensate for the mean behavior of the system jumps via an additional deterministic term. Editor: N.U. Ahmed     

The optimal stochastic control of an epitaxial process unit

The problem of computerized batch control of the silicon epitaxial layer deposition technological process has been solved using optimal stochastic control methods. A control algorithm is presented the main emphasis being given to the forecasting and compensating of disturbing processes which act on a process unit under real operation conditions. The method of multidimensional time series, stochastic model form identification for the process noise is developed based on multidimensional time series, correlation analysis results. The “maximum likelihood” identification method is applied in order to obtain efficient estimates of the model parameters. The identification of the model form and model parameters is carried out on the basis of a rather extensive set of data obtained from operation records of a high capacity epitaxial unit. The adequacy of the identified models is checked by means of a correlation analysis of the model residuals. It is demonstrated that results comparable to those with an intuitive process control by an experienced operator, can be achieved when using the algorithm presented in the present work for process computer control. This algorithm thus represents a reliable and rational basis for process control computer software development.     

GPU-based optimal control for RWM feedback in tokamaks

The design and implementation of a Graphics Processing Unit (GPU) based Resistive Wall Mode (RWM) controller to perform feedback control on the RWM using Linear Quadratic Gaussian (LQG) control is reported herein. The control algorithm is based on a simplified DIII-D VALEN model. By using NVIDIA’s GPUDirect RDMA framework, the digitizer and output module are able to write and read directly to and from GPU memory, eliminating memory transfers between host and GPU. The system and algorithm was able to reduce plasma response excited by externally applied fields by 32% during development experiments.     

Implications of dissipativity,inverse optimal control,and stability margins for nonlinear stochastic feedback regulators

In this paper, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton‐Jacobi‐Bellman controllers that minimize a nonlinear‐nonquadratic performance criterion with cross‐weighting terms. Furthermore, using the newly developed notion of stochastic dissipativity, we derive a return difference inequality to provide connections between stochastic dissipativity and optimality of nonlinear controllers for stochastic dynamical systems. In particular, using extended Kalman‐Yakubovich‐Popov conditions characterizing stochastic dissipativity, we show that our optimal feedback control law satisfies a return difference inequality predicated on the infinitesimal generator of a controlled Markov diffusion process if and only if the controller is stochastically dissipative with respect to a specific quadratic supply rate.     

Sensitivity reducing observers for optimal feedback control

This paper considers the problem of designing an observer for use in a linear quadratic optimal feedback control scheme so as to minimize the effects of small departures in the plant parameters from their nominal values.     

Robust optimal control during feedback disruption for nonlinear systems controlled by an observer-based output feedback controller

In this paper, a robust optimal control problem during feedback disruption is considered for a class of nonlinear systems which have been controlled by an observer-based output feedback controller. It is shown that during feedback disruption, there exists an optimal control input which keeps both system states and observer errors within a specified bound for the longest time. Then, it is shown that such an optimal control input can be practically implemented by using a bang-bang control input in terms of control performance. One numerical and one practical examples are given for clear illustration.     

An existence theorem for discrete-time infinite-horizon optimal control problems

An existence theorem is given for a general class of deterministic, infinite-horizon, discrete-time optimal control problems. The hypotheses of the theorem are weak and can be easily verified. The objective function may be either a summation or supremum over time.     

Polynomial optimization of stochastic feedback control for unstable plants

The role of Ku?era's two diophantine equations is explored in the optimization of a discrete-time feedback controller for a multivariate unstable plant subject to stochastic reference and disturbance, but it is usually only necessary to solve one of the equations. However, with an unstable plant, an extra diophantine equation must be solved when there is output measurement noise.     

Low-sensitivity optimal feedback control for linear discrete-time systems

The problem of reducing sensitivity of discrete-time systems to parameter variations is considered. State and output feedback gains are obtained to minimize a quadratic criterion which includes sensitivity functions. Necessary conditions for optimality are derived and numerical examples are discussed.     

Descent algorithms for optimal periodic output feedback control

Periodic output feedback is investigated in the context of linear-quadratic regulation for finite-dimensional time-invariant linear systems. Discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control. The optimal solution is obtained in two steps by separating the continuous-time from the discrete-time structure. First, the optimal pole placement problem under periodic output feedback is solved explicitly under the assumption that the behavior at the sample times has been specified in terms of a gain matrix G. Then the minimum value, which depends on G, is substituted into the overall objective. This results in a finite-dimensional nonlinear programming problem over all admissible gain matrices G. The solution defines the optimal periodic output feedback control via the formulas of the optimal pole placement problem. A steepest descent and a direct iterative method for solving this problem are formulated and compared. Numerical examples show that the performance using periodic output feedback is almost equivalent to that using optimal continuous-state feedback     

Discrete-time optimal control for stochastic nonlinear polynomial systems

This paper presents a solution to the discrete-time optimal control problem for stochastic nonlinear polynomial systems over linear observations and a quadratic criterion. The solution is obtained in two steps: the optimal control algorithm is developed for nonlinear polynomial systems by considering complete information when generating a control law. Then, the state estimate equations for discrete-time stochastic nonlinear polynomial system over linear observations are employed. The closed-form solution is finally obtained substituting the state estimates into the obtained control law. The designed optimal control algorithm can be applied to both distributed and lumped systems. To show effectiveness of the proposed controller, an illustrative example is presented for a second degree polynomial system. The obtained results are compared to the optimal control for the linearized system.     

A second-order feedback method for optimal control computations

A second-order method for computing optimal control is described. The method computes control corrections from the state perturbations through feedback coefficients. On each successive trajectory a test is made for a conjugate point, and the algorithm automatically forms a control correction when such points occur. Unlike some earliermethods, terminal constraints of arbitrary dimensions are handled by the method. Numerical results for two cases of a non-linear example based on van der Pol's equation are included.     

On a result in stochastic optimal control

In a recent paper an equivalence was demonstrated between a certain stochastic optimal control problem and a linear-quadratic game. In this note it is pointed out that a more general equivalence exists which has an interesting form.     

Necessary and sufficient conditions for optimal control of stochastic systems associated with Lévy processes

The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel’s martingales and an independent multi-dimensional Brownian motion. Necessary and sufficient conditions for an optimal control of the control problem with the control domain being convex are proved by the classical method of convex variation, and the coefficients appearing in the systems are allowed to depend on the control variables. As an application, the linear quadratic stochastic optimal control problem is studied.     

Dynamic output feedback control synthesis for stochastic time-delay systems

This article deals with the dynamic output feedback control synthesis problem for Itô-type stochastic time-delay systems. Our aim is to design a full order dynamic output feedback controller to achieve the desired control objectives. We will formulate the controller design problem as an H _∞ optimisation problem in the mean-square sense. The main contributions of this article are as follows: (i) for stochastic systems, the design of a controller with multiple objectives can be addressed without employing a unique Lyapunov function; (ii) using an inequality technique and Finsler Lemma, we provide convex controller synthesis conditions described by linear matrix inequalities (LMIs). Some examples are presented to show the effectiveness of the developed theoretical results.     

Output feedback gains for a linear-discrete stochastic control problem

For the finite-horizon linear-discrete quadratic stochastic control problem, the control is restricted to be a memoryless linear transformation of the measurement. The two-point boundary value problem that specifies the feedback gain matrices is derived, and an algorithm for solving it is given. An example is solved comparing the cost of the suboptimal control to the optimal control.