Showing papers on "Optimal control published in 1993"
TL;DR: This paper presents a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error, and requires considerably less online computation than existingReceding horizon controllers for nonlinear, constrained systems.
Abstract: We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems. >
1,163 citations
Book•
01 Jan 1993TL;DR: In this paper, the authors present a semi-group method for systems with unbounded control and Observation Operators Differential Systems with Delays (DOS) with delays.
Abstract: Preface to the Second Edition Preface to Volume I of the First Edition Preface to Volume II of the First Edition List of Figures Introduction Part I. Finite Dimensional Linear Control of Dynamical Systems Control of Linear Finite Dimensional Differential Systems Linear Quadratic Two-Person Zero-Sum Differential Games Part II. Representation of Infinite Dimensional Linear Control Dynamical Systems Semi-groups of Operators and Interpolation Variational Theory of Parabolic Systems Semi-group Methods for Systems with Unbounded Control and Observation Operators Differential Systems with Delays Part III. Qualitative Properties of Linear Control Dynamical Systems Controllability and Observability for a Class of Infinite Dimensional Systems Part IV. Quadratic Optimal Control: Finite Time Horizon Systems with Bounded Control Operators: Control Inside the Domain Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary Part V. Quadratic Optimal Control: Infinite Time Horizon Systems with Bounded Control Operators: Control Inside the Domain Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary Appendix A. An Isomorphism Result References Index
945 citations
TL;DR: A survey of the average cost control problem for discrete-time Markov processes can be found in this paper, where the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades.
Abstract: This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.
619 citations
01 Feb 1993
TL;DR: The authors present algorithms for robotic (eye-in-hand configuration) real-time visual tracking of arbitrary 3D objects traveling at unknown velocities in a 2D space (depth is given as known).
Abstract: The authors present algorithms for robotic (eye-in-hand configuration) real-time visual tracking of arbitrary 3D objects traveling at unknown velocities in a 2D space (depth is given as known). Visual tracking is formulated as a problem of combining control with computer vision. A mathematical formulation of the control problem that includes information from a novel feedback vision sensor and represents everything with respect to the camera frame is presented. The sum-of-squared differences (SSD) optical flow is used to compute the vector of discrete displacements each instant of time. These displacements can be fed either directly to a PI (proportional-integral) controller or to a pole assignment controller or discrete steady-state Kalman filter. In the latter case, the Kalman filter calculates the estimated values of the system's states and the exogenous disturbances, and a discrete LQG (linear-quadratic Gaussian) controller computes the desired motion of the robotic system. The outputs of the controllers are sent to the Cartesian robotic controller. Performance results are presented. >
613 citations
Book•
01 Jan 1993
TL;DR: In this paper, nonlinear operators of monotone type controlled elliptical variational inequalities nonlinear accretive differential equations optimal control of parabolic variational inequality optimal control in real time.
Abstract: Nonlinear operators of monotone type controlled elliptical variational inequalities nonlinear accretive differential equations optimal control of parabolic variational inequalities optimal control in real time.
565 citations
Book•
14 Jun 1993
TL;DR: In this article, Hadamard and tykhonov well-posedness in optimal control and the calculus of variations were defined. But they were not defined in the context of mathematical programming.
Abstract: Tykhonov well-posedness.- Hadamard and tykhonov well-posedness.- Generic well-posedness.- Well-posedness and variational, epi- and mosco convergences.- Well-posedness in optimal control.- Relaxation and value hadamard well-posedness in optimal control.- Singular perturbations in optimal control.- Well-posedness in the calculus of variations.- Hadamard well-posedness in mathematical programming.
453 citations
TL;DR: This work considers the simplified case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds, and provides the first provably good approximation algorithm, and shows that it runs in polynomial time.
Abstract: Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimal-time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simplified case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be flown from a start to a goal, amidst polyhedral obstacles in 2D or 3D. Although exact solutions to this problem are not known, we provide the first provably good approximation algorithm, and show that it runs in polynomial time
438 citations
TL;DR: In this paper, a new algorithm using the primal-dual interior point method with the predictor-corrector for solving nonlinear optimal power flow (OPF) problems is presented.
Abstract: A new algorithm using the primal-dual interior point method with the predictor-corrector for solving nonlinear optimal power flow (OPF) problems is presented. The formulation and the solution technique are new. Both equalities and inequalities in the OPF are considered and simultaneously solved in a nonlinear manner based on the Karush-Kuhn-Tucker (KKT) conditions. The major computational effort of the algorithm is solving a symmetrical system of equations, whose sparsity structure is fixed. Therefore only one optimal ordering and one symbolic factorization are involved. Numerical results of several test systems ranging in size from 9 to 2423 buses are presented and comparisons are made with the pure primal-dual interior point algorithm. The results show that the predictor-corrector primal-dual interior point algorithm for OPF is computationally more attractive than the pure primal-dual interior point algorithm in terms of speed and iteration count. >
422 citations
01 Jan 1993
TL;DR: In this paper, the convergence properties of the discretization of control and state variables are derived and used to obtain reliable estimates of adjoint variables in the presence of active state constraints, which can be improved by including the switching structure of the state constraint into the optimization procedure.
Abstract: By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQP-methods [10]. Convergence properties of the discretization are derived. Prom a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented.
346 citations
TL;DR: In this paper, a continuous time deterministic optimal preview control algorithm is applied to the lateral guidance of a vehicle for an automated highway, where the front wheel steering angle of the vehicle is controlled so that the vehicle follows the center for a lane with small tracking error and maintains good ride quality simultaneously.
Abstract: The continuous time deterministic optimal preview control algorithm is applied to the lateral guidance of a vehicle for an automated highway. In the lateral guidance problem, the front wheel steering angle of the vehicle is controlled so that the vehicle follows the center for a lane with small tracking error and maintains good ride quality simultaneously. A preview control algorithm is obtained by minimizing a quadratic performance index which includes terms representing the passenger ride quality as well as the lateral tracking error, each of these terms is multiplied by a frequency dependent weight. It is shown that the optimal preview control law consists of a feedback control term and two feedforward control terms. The feedforward preview control action significantly improves the tracking performance and ride quality. Frequency-domain analyses, as well as numerical simulation results, show the improvements achieved by using the preview control algorithm in both the frequency and time domains.
315 citations
01 Jan 1993
TL;DR: In this paper, a survey of theoretical and practical results connected with sufficient conditions for global optimality of controlled dynamic processes is presented, both discrete and continuous time systems and systems with distributed parameters are discussed.
Abstract: The paper contains a survey of theoretical and practical results connected with sufficient conditions for global optimality of controlled dynamic processes. Both discrete and continuous time systems and systems with distributed parameters are discussed.
TL;DR: This survey is a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems and a simple parametrization of all stabilizing controllers for a given plant is presented.
01 Jan 1993
TL;DR: The Legendre condition as discussed by the authors is a necessary condition for the solution of the Euler equation (16.1), and the Transversality condition is sufficient for the transversality.
Abstract: The Euler equation. A necessary condition for the solution of (16.1). An alternative form of the Euler equation. The Legendre condition. A necessary condition for the solution of (16.1). Sufficient conditions for the solution of (16.1). Transversality condition. Adding condition (16.5) gives sufficient conditions.
TL;DR: In this paper, the existence of a homogeneous Markov nonrandomized optimal policy is established by a convex analytic method using a controlled switching diffusion model to study the hierarchical control of flexible manufacturing systems.
Abstract: A controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems The existence of a homogeneous Markov nonrandomized optimal policy is established by a convex analytic method Using the existence of such a policy, the existence of a unique solution in a certain class to the associated Hamilton-Jacobi-Bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate Hamiltonian
TL;DR: In this paper, the value function of Mayer's problem arising in optimal control is investigated, and lower semicontinuous solutions of the associated Hamilton-Jacobi-Bellman equation are defined in three (equivalent) ways.
Abstract: The value function of Mayer’s problem arising in optimal control is investigated, and lower semicontinuous solutions of the associated Hamilton–Jacobi–Bellman equation are defined in three (equivalent) ways. Under quite weak assumptions about the control system, the value function is the unique solution. Moreover, it is stable with respect to perturbations of the control system and the cost. It coincides with the viscosity solution whenever it is continuous.
TL;DR: The paper surveys applications of optimal control techniques to the design of active suspensions, starting from simple quarter-car, 1D models, which are followed by their half-Car, 2D, and full- car, 3D, counterparts.
Abstract: The paper surveys applications of optimal control techniques to the design of active suspensions, starting from simple quarter-car, 1D models, which are followed by their half-car, 2D, and full-car, 3D, counterparts. The emphasis is on Linear-Quadratic (LQ) optimal control and automotive vehicles
TL;DR: In this paper, the authors studied the problem of keeping the exchange rate in a target zone with discrete interventions and proved that there exists an optimal control if the cost associated with each control is a fixed cost plus a proportional cost.
Abstract: We control a diffusion process with constant coefficients in order to keep this process in a given band with impulse control methods. We prove that there exists an optimal control if the cost associated with each control is a fixed cost plus a proportional cost. We study the problem of the exchange rate and prove that it is possible to keep the exchange rate in a target zone with discrete interventions.
TL;DR: In this paper, state constrained optimal control problems of semilinear elliptic equations, the control being on the boundary, are studied. Optimality conditions are derived and regularity of the control is established.
Abstract: This paper is concerned with state constrained optimal control problems of semilinear elliptic equations, the control being on the boundary. Optimality conditions are derived and regularity of the ...
TL;DR: Using the optimal control theory approach, two new DUO traffic assignment models for a congested transportation network are formulated, including new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model.
Abstract: The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints...
TL;DR: Keywords .
TL;DR: This work reviews models for the optimal control of networks of queues based on Markov decision theory and the characterization of the structure of optimal control policies.
Abstract: We review models for the optimal control of networks of queues. Our main emphasis is on models based on Markov decision theory and the characterization of the structure of optimal control policies.
TL;DR: In this article, the authors apply mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows.
Abstract: The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.
Book•
01 Jan 1993
TL;DR: In this paper, the Maximimum Principal Principal of PonTRYAGIN is presented as a proof of the maximality of the maximum principle of PonsTRYAGI.
Abstract: PART 2: OPTIMIZATION IN PART 3: THE CALCULUS OF VARIATIONS PART 4: OPTIMAL CONTROL I: THEORY PART 5: OPTIMAL CONTROL II: APPLICATIONS PART 6: PROOF OF THE MAXIMUM PRINCIPLE OF PONTRYAGIN
Book•
01 Sep 1993
TL;DR: In this book, the full theory of differential games of pursuit with complete and partial information is developed and new time-consistent optimality principles in the n-person differential game theory are introduced and investigated.
Abstract: The classical optimal control theory deals with the determination of an optimal control that optimizes the criterion subject to the dynamic constraint expressing the evolution of the system state under the influence of control variables. If this is extended to the case criteria (payoff function) it is possible to begin to explore differential games. Zero-sum differential games, also called differential games of pursuit, constitute the most developed part of differential games and are rigorously investigated. In this book, the full theory of differential games of pursuit with complete and partial information is developed. Numerous concrete pursuit-evasion games are solved ("life-line" game, simple pursuit games, etc) and new time-consistent optimality principles in the n-person differential game theory are introduced and investigated.
TL;DR: In this article, it is shown that under appropriate mean square detectability and stability conditions the infinite horizon optimal control problem for the general case of Markovian jump linear quadratic systems has a unique solution when the control system is mean square stable.
Abstract: The research is oriented to the control of discrete — time linear systems with randomly changing parameters which can be described by a finite — state Markov chain. The cost critrion is a quadratic form of the controls and states of the system. The criterion parameters also depend on the states of the Markov chain. Two models of observation of the Markov chain are adopted — delay for one step and undelay. It is shown that under appropriate mean square detectability and stability conditions the infinite horizon optimal control problem for the general case of Markovian jump linear quadratic systems has a unique solution when the control system is mean square stable. Necessary and sufficient conditions are given to determine if a system is mean square stable.
Dissertation•
01 Jan 1993
Book•
23 Apr 1993
TL;DR: In this paper, the authors present an approach for automated structural optimization using nonlinear programming and linear programming, with the objective of reducing the number of parameters to be used by the algorithm.
Abstract: 1 Problem Statement.- 1.1 Introduction.- 1.1.1 Automated Structural Optimization.- 1.1.2 Structural Optimization Methods.- 1.1.3 Historical Perspective.- 1.1.4 Scope of Text.- 1.2 Analysis Models.- 1.2.1 Elastic Analysis.- 1.2.2 Plastic Analysis.- 1.3 General Formulation.- 1.3.1 Design Variables.- 1.3.2 Constraints.- 1.3.3 Objective Function.- 1.3.4 Mathematical Formulation.- 1.4 Typical Problem Formulations.- 1.4.1 Displacement Method Formulations.- 1.4.2 Force Method Formulations.- Exercises.- 2 Optimization Methods.- 2.1 Optimization Concepts.- 2.1.1 Unconstrained Minimum.- 2.1.2 Constrained Minimum.- 2.2 Unconstrained Minimization.- 2.2.1 Minimization Along a Line.- 2.2.2 Minimization of Functions of Several Variables.- 2.3 Constrained Minimization: Linear Programming.- 2.3.1 Introduction.- 2.3.2 Problem Formulation.- 2.3.3 Method of Solution.- 2.3.4 Further Considerations.- 2.4 Constrained Minimization: Nonlinear Programming.- 2.4.1 Sequential Unconstrained Minimization.- 2.4.2 The Method of Feasible Directions.- 2.4.3 Other Methods.- Exercises.- 3 Approximation Concepts.- 3.1 General Approximations.- 3.1.1 Design Sensitivity Analysis.- 3.1.2 Intermediate Variables.- 3.1.3 Sequential Approximations.- 3.2 Approximate Behavior Models.- 3.2.1 Basic Displacement Approximations.- 3.2.2 Combined Displacement Approximations.- 3.2.3 Homogeneous Functions.- 3.2.4 Displacement Approximations along a Line.- 3.2.5 Approximate Force Models.- Exercises.- 4 Design Procedures.- 4.1 Linear Programming Formulations.- 4.1.1 Plastic Design.- 4.1.2 Elastic Design.- 4.2 Feasible-Design Procedures.- 4.2.1 General Considerations.- 4.2.2 Optimization in Design Planes.- 4.3 Optimality Criteria Procedures.- 4.3.1 Stress Criteria.- 4.3.2 Displacement Criteria.- 4.3.3 Design Procedures.- 4.3.4 The Relationship Between OC and MP.- 4.4 Multilevel Optimal Design.- 4.4.1 General Formulation.- 4.4.2 Two-Level Design of Prestressed Concrete Systems.- 4.4.3 Multilevel Design of Indeterminate Systems.- 4.5 Optimal Design and Structural Control.- 4.5.1 Optimal Control of Structures.- 4.5.2 Improved Optimal Design by Structural Control.- 4.6 Geometrical Optimization.- 4.6.1 Simultaneous Optimization of Geometry and Cross Sections.- 4.6.2 Approximations and Multilevel Optimization.- 4.7 Topological Optimization.- 4.7.1 Problem Statement.- 4.7.2 Types of Optimal Topologies.- 4.7.3 Properties of Optimal Topologies.- 4.7.4 Approximations and Two-Stage Procedures.- 4.8 Interactive Layout Optimization.- 4.8.1 Optimization Programs.- 4.8.2 Graphical Interaction Programs.- 4.8.3 Design Procedure.- Exercises.- References.
TL;DR: It is shown that as the singular perturbation parameter ϵ approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbances attenuation levels for the slow and fast subsystems under appropriate "slow" and "fast"quadratic cost functions.
TL;DR: This book is a significant contribution to the problem of modelling, estimation and adaptive control of bioreactors and is a highly valuable document, useful not only for biotechnological engineers, but also for all control engineers having to address issues regarding nonlinear and/or nonstationary processes.
TL;DR: This work describes interior point algorithms for a discrete-time linear-quadratic regulator problem with mixed state/control constraints and shows how they can be efficiently-incorporated into an inexact sequential quadratic programming algorithm for nonlinear problems.
Abstract: We show that recently developed interior point methods for quadratic programming and linear complementarity problems can be put to use in solving discrete-time optimal control problems, with general pointwise constraints on states and controls. We describe interior point algorithms for a discrete-time linear-quadratic regulator problem with mixed state/control constraints and show how they can be efficiently-incorporated into an inexact sequential quadratic programming algorithm for nonlinear problems. The key to the efficiency of the interior-point method is the narrow-banded structure of the coefficient matrix which is factorized at each iteration.