Anticipation in discrete-time LQ control. I. Open-loop control
Contrôle interne exact des vibrations d'une plaque rectangulaire
Controllability, observability and optimal control of continuous-time 2-D systems
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data....
Deadbeat control, pole placement, and LQ regulation
Deadbeat control, a typical example of linear control strategies in discrete- time systems, is shown to be a special case of the linear-quadratic regulation. This result is obtained by drawing on the parallels between the state-space and the transfer-function design techniques.
Decentralized control of linear dynamical systems with partial aggregation
Design of predictive LQ controller
A single variable controller is developed in the predictive control framework based upon minimisation of the LQ criterion with infinite output and control horizons. The infinite version of the predictive cost function results in better stability properties of the controller and still enables to incorporate constraints into the control design. The constrained controller consists of two parts: time-invariant nominal LQ controller and time-variant part given by Youla–Kučera parametrisation of all stabilising...
Design of robust output affine quadratic controller
The paper addresses the problem robust output feedback controller design with guaranteed cost and affine quadratic stability for linear continuous time affine systems. The proposed design method leads to a non-iterative LMI based algorithm. A numerical example is given to illustrate the design procedure.
Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions
In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative () and integration matrix () are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...
Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises
This paper is concerned with the sampled-data based adaptive linear quadratic (LQ) control of hybrid systems with both unmeasurable Markov jump processes and stochastic noises. By the least matching error estimation algorithm, parameter estimates are presented. By a double-step (DS) sampling approach and the certainty equivalence principle, a sampled-data based adaptive LQ control is designed. The DS-approach is characterized by a comparatively large estimation step for parameter estimation and...
Double-stepped adaptive control for hybrid systems with unknown Markov jumps and stochastic noises
This paper is concerned with the sampled-data based adaptive linear quadratic (LQ) control of hybrid systems with both unmeasurable Markov jump processes and stochastic noises. By the least matching error estimation algorithm, parameter estimates are presented. By a double-step (DS) sampling approach and the certainty equivalence principle, a sampled-data based adaptive LQ control is designed. The DS-approach is characterized by a comparatively large estimation step for parameter estimation and...
Duality in the optimal control for damped hyperbolic systems with positive control.
Duality in the optimal control of hyperbolic equations with positive controls.
Epi/hypo-convergence: The slice topology and saddle points approximation.
Equivalent cost functionals and stochastic linear quadratic optimal control problems
This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear...
Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion
A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system...
Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
Existence and uniqueness of constrained globally optimal feedback controls in a linear-quadratic framework.
Finite element error analysis for state-constrained optimal control of the Stokes equations
Fixed poles of optimal control by measurement feedback
This paper is concerned with the flexibility in the closed loop pole location when solving the optimal control problem (also called the optimal disturbance attenuation problem) by proper measurement feedback. It is shown that there exists a precise and unique set of poles which is present in the closed loop system obtained by any measurement feedback solution of the optimal control problem. These “ optimal fixed poles” are characterized in geometric as well as structural terms. A procedure...
Flow control in connection-oriented networks: a time-varying sampling period system case study
In this paper congestion control problem in connection-oriented communication network with multiple data sources is addressed. In the considered network the feedback necessary for the flow regulation is provided by means of management units, which are sent by each source once every M data packets. The management units, carrying the information about the current network state, return to their origin round trip time RTT after they were sent. Since the source rate is adjusted only at the instant of...