Showing papers on "Optimal control published in 2001"

Modern Control Engineering

Abstract: Introduction to automatic control systems mathematical background mathematical models of systems classical time-domain analysis of control systems state-space analysis of control systems stability the root locus method frequency domain analysis classical control design methods state-space design methods optimal control digital control system identification adaptive control robust control fuzzy control. Appendices: Laplace transform tables the Z-transform transform tables.

Stabilization of linear systems with limited information

Abstract: We show that the coarsest, or least dense, quantizer that quadratically stabilizes a single input linear discrete time invariant system is logarithmic, and can be computed by solving a special linear quadratic regulator problem. We provide a closed form for the optimal logarithmic base exclusively in terms of the unstable eigenvalues of the system. We show how to design quantized state-feedback controllers, and quantized state estimators. This leads to the design of hybrid output feedback controllers. The theory is then extended to sampling and quantization of continuous time linear systems sampled at constant time intervals. We generalize the definition of density of quantization to the density of sampling and quantization in a natural way, and search for the coarsest sampling and quantization scheme that ensures stability. Finally, by relaxing the definition of quadratic stability, we show how to construct logarithmic quantizers with only finite number of quantization levels and still achieve practical stability of the closed-loop system.

An optimal control approach to a posteriori error estimation in finite element methods

Abstract: This article surveys a general approach to error control and adaptive mesh design in Galerkin finite element methods that is based on duality principles as used in optimal control. Most of the existing work on a posteriori error analysis deals with error estimation in global norms like the ‘energy norm’ or the L2 norm, involving usually unknown ‘stability constants’. However, in most applications, the error in a global norm does not provide useful bounds for the errors in the quantities of real physical interest. Further, their sensitivity to local error sources is not properly represented by global stability constants. These deficiencies are overcome by employing duality techniques, as is common in a priori error analysis of finite element methods, and replacing the global stability constants by computationally obtained local sensitivity factors. Combining this with Galerkin orthogonality, a posteriori estimates can be derived directly for the error in the target quantity. In these estimates local residuals of the computed solution are multiplied by weights which measure the dependence of the error on the local residuals. Those, in turn, can be controlled by locally refining or coarsening the computational mesh. The weights are obtained by approximately solving a linear adjoint problem. The resulting a posteriori error estimates provide the basis of a feedback process for successively constructing economical meshes and corresponding error bounds tailored to the particular goal of the computation. This approach, called the ‘dual-weighted-residual method’, is introduced initially within an abstract functional analytic setting, and is then developed in detail for several model situations featuring the characteristic properties of elliptic, parabolic and hyperbolic problems. After having discussed the basic properties of duality-based adaptivity, we demonstrate the potential of this approach by presenting a selection of results obtained for practical test cases. These include problems from viscous fluid flow, chemically reactive flow, elasto-plasticity, radiative transfer, and optimal control. Throughout the paper, open theoretical and practical problems are stated together with references to the relevant literature.

Parameterized linear matrix inequality techniques in fuzzy control system design

Abstract: This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems. These PLMI characterizations are, in turn, relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control systems. The advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations.

Time optimal control in spin systems

Abstract: In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.

Simulation and Optimization in an AGC System after Deregulation

Abstract: In this paper, the traditional automatic generation control (AGC) two-area system is modified to take into account the effect of bilateral contracts on the dynamics. The concept of distribution companies (DISCO) participation matrix to simulate these bilateral contracts is introduced and reflected in the two-area block diagram. Trajectory sensitivities are used to obtain optimal parameters of the system using a gradient Newton algorithm.

DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms

Abstract: Direct numerical simulations (DNS) and optimal control theory are used in a predictive control setting to determine controls that effectively reduce the turbulent kinetic energy and drag of a turbulent flow in a plane channel at Reτ = 100 and Reτ = 180. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. The algorithm used for the control optimization is based solely on the control objective and the nonlinear partial differential equation governing the flow, with no ad hoc assumptions other than the finite prediction horizon, T, over which the control is optimized.Flow relaminarization, accompanied by a drag reduction of over 50%, is obtained in some of the control cases with the predictive control approach in direct numerical simulations of subcritical turbulent channel flows. Such performance far exceeds what has been obtained to date in similar flows (using this type of actuation) via adaptive strategies such as neural networks, intuition-based strategies such as opposition control, and the so-called ‘suboptimal’ strategies, which involve optimizations over a vanishingly small prediction horizon T+ → 0. To achieve flow relaminarization in the predictive control approach, it is shown that it is necessary to optimize the controls over a sufficiently long prediction horizon T+ [gsim ] 25. Implications of this result are discussed.The predictive control algorithm requires full flow field information and is computationally expensive, involving iterative direct numerical simulations. It is, therefore, impossible to implement this algorithm directly in a practical setting. However, these calculations allow us to quantify the best possible system performance given a certain class of flow actuation and to qualify how optimized controls correlate with the near-wall coherent structures believed to dominate the process of turbulence production in wall-bounded flows. Further, various approaches have been proposed to distil practical feedback schemes from the predictive control approach without the suboptimal approximation, which is shown in the present work to restrict severely the effectiveness of the resulting control algorithm. The present work thus represents a further step towards the determination of optimally effective yet implementable control strategies for the mitigation or enhancement of the consequential effects of turbulence.

Design of optimal disturbance rejection PID controllers using genetic algorithms

Abstract: This paper presents a method to design an optimal disturbance rejection PID controller. First, a condition for disturbance rejection of a control system-H/sub /spl infin//-norm-is described. Second, the design is formulated as a constrained optimization problem. It consists of minimizing a performance index, i.e., the integral of the time weighted squared error subject to the disturbance rejection constraint. A new method employing two genetic algorithms (GA) is developed for solving the constraint optimization problem. The method is tested by a design example of a PID controller for a servomotor system. Simulation results are presented to demonstrate the performance and validity of the method.

An optimal fuzzy PID controller

Abstract: This paper introduces an optimal fuzzy proportional-integral-derivative (PID) controller. The fuzzy PID controller is a discrete-time version of the conventional PID controller, which preserves the same linear structure of the proportional, integral, and derivative parts but has constant coefficient yet self-tuned control gains. Fuzzy logic is employed only for the design; the resulting controller does not need to execute any fuzzy rule base, and is actually a conventional PID controller with analytical formulae. The main improvement is in endowing the classical controller with a certain adaptive control capability. The constant PID control gains are optimized by using the multiobjective genetic algorithm (MOGA), thereby yielding an optimal fuzzy PID controller. Computer simulations are shown to demonstrate its improvement over the fuzzy PID controller without MOGA optimization.

Distributed model predictive control

Abstract: We explore a distributed model predictive control (DMPC) scheme. The controllers apply model predictive control (MPC) policies to their local subsystems. They exchange their predictions by communication and incorporate the information from other controllers into their local MPC problem so as to coordinate with each other. For the full local state feedback and one-step delayed prediction exchange case, stability is ensured for controllable systems satisfying a matching condition by imposing stability constraints on the next state in the prediction. An example of multi-area load-frequency control is used as an example application for this DMPC scheme to show the performance of the scheme.

Unconstrained receding-horizon control of nonlinear systems

Abstract: It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted.

Optimal control of a class of hybrid systems

Abstract: We present a modeling framework for hybrid systems intended to capture the interaction of event-driven and time-driven dynamics. This is motivated by the structure of many manufacturing environments where discrete entities (termed jobs) are processed through a network of workcenters so as to change their physical characteristics. Associated with each job is a temporal state subject to event-driven dynamics and a physical state subject to time-driven dynamics. Based on this framework, we formulate and analyze a class of optimal control problems for single-stage processes. First-order optimality conditions are derived and several properties of optimal state trajectories (sample paths) are identified which significantly simplify the task of obtaining explicit optimal control policies.

Autonomous helicopter control using reinforcement learning policy search methods

Abstract: Many control problems in the robotics field can be cast as partially observed Markovian decision problems (POMDPs), an optimal control formalism. Finding optimal solutions to such problems in general, however is known to be intractable. It has often been observed that in practice, simple structured controllers suffice for good sub-optimal control, and recent research in the artificial intelligence community has focused on policy search methods as techniques for finding sub-optimal controllers when such structured controllers do exist. Traditional model-based reinforcement learning algorithms make a certainty equivalence assumption on their learned models and calculate optimal policies for a maximum-likelihood Markovian model. We consider algorithms that evaluate and synthesize controllers under distributions of Markovian models. Previous work has demonstrated that algorithms that maximize mean reward with respect to model uncertainty leads to safer and more robust controllers. We consider briefly other performance criterion that emphasize robustness and exploration in the search for controllers, and note the relation with experiment design and active learning. To validate the power of the approach on a robotic application we demonstrate the presented learning control algorithm by flying an autonomous helicopter. We show that the controller learned is robust and delivers good performance in this real-world domain.

Optimal Capacitor Placement in Radial Distribution Networks

Abstract: The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations, and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a nonpolynomial time (NP) complete problem, the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

Optimal Proportional Reinsurance Policies in a Dynamic Setting

Abstract: We consider dynamic proportional reinsurance strategies and derive the optimal strategies in a diffusion setup and a classical risk model. Optimal is meant in the sense of minimizing the ruin probability. Two basic examples are discussed.

Torque-maximizing field-weakening control: design, analysis, and parameter selection

Abstract: The torque-maximizing field-weakening control scheme proposed by Kim and Sul is developed further. The performance under imperfect field orientation conditions is investigated, and it is shown that an overestimated-rather than an underestimated-model leakage inductance should be used. A slightly modified algorithm, which offers better robustness and reduced computational complexity, is presented. The importance, for good performance, of combining the scheme with current and speed controllers featuring antiwindup and improved disturbance rejection is emphasized. The dynamics of the resulting closed-loop system are analyzed. Obtained in the process, are rules for selection of all controller parameters, allowing tuning without trial-and error steps. Good performance of the resulting system is verified experimentally.

Online optimization of large scale systems

Abstract: I Optimal Control for Ordinary Differential Equations.- Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods.- Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints.- Real-Time Control of an Industrial Robot under Control and State Constraints.- Real-Time Optimal Control of Shape Memory Alloy Actuators in Smart Structures.- Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy.- Real-Time Optimization of DAE Systems.- Real-Time Solutions of Bang-Bang and Singular Optimal Control Problems.- Conflict Avoidance During Landing Approach Using Parallel Feedback Control.- II Optimal Control for Partial Differential Equations.- Optimal Control Problems with a First Order PDE System - Necessary and Sufficient Optimality Conditions.- Optimal Control Problems for the Nonlinear Heat Equation.- Fast Optimization Methods in the Selective Cooling of Steel.- Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements.- Instantaneous Control of Vibrating String Networks.- Modelling, Stabilization, and Control of Flow in Networks of Open Channels.- Optimal Control of Distributed Systems with Break Points.- to Model Based Optimization of Chemical Processes on Moving Horizons.- Multiscale Concepts for Moving Horizon Optimization.- Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column.- Towards Nonlinear Model-Based Predictive Optimal Control of Large-Scale Process Models with Application to Air Separation Plants.- IV Delay Differential Equations in Medical Decision Support Systems.- Differential Equations with State-Dependent Delays.- Biomathematical Models with State-Dependent Delays for Granulocytopoiesis.- Stochastic Optimization for Operating Chemical Processes under Uncertainty.- A Multistage Stochastic Programming Approach in Real-Time Process Control.- Optimal Control of a Continuous Distillation Process under Probabilistic Constraints.- Adaptive Optimal Stochastic Trajectory Planning.- Stochastic Optimization Methods in Robust Adaptive Control of Robots.- Multistage Stochastic Integer Programs: An Introduction.- Decomposition Methods for Two-Stage Stochastic Integer Programs.- Modeling of Uncertainty for the Real-Time Management of Power Systems.- Online Scheduling of Multiproduct Batch Plants under Uncertainty.- VIII Combinatorial Online Planning in Transportation.- Combinatorial Online Optimization in Real Time.- Online Optimization of Complex Transportation Systems.- Stowage and Transport Optimization in Ship Planning.- IX Real-Time Annealing in Image Segmentation.- Basic Principles of Annealing for Large Scale Non-Linear Optimization.- Multiscale Annealing and Robustness: Fast Heuristics for Large Scale Non-linear Optimization.- Author Index.

A Posteriori Error Estimates for Distributed Convex Optimal Control Problems

Abstract: In this paper, we present an a posteriori error analysis for finite element approximation of distributed convex optimal control problems. We derive a posteriori error estimates for the coupled state and control approximations under some assumptions which hold in many applications. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for control problems. Explicit estimates are obtained for some model problems which frequently appear in real-life applications.

Energy management strategy for a parallel hybrid electric truck

Abstract: Due to the complex nature of hybrid electric vehicles, control strategies based on engineering intuition frequently fail to achieve satisfactory overall system efficiency. This paper presents a procedure for improving the energy management strategy for a parallel hybrid electric truck on the basis of dynamic optimization over a given drive cycle. Dynamic programming techniques are utilized to determine the optimal control actions for a hybrid powertrain in order to minimize fuel consumption. By carefully analyzing the resulting optimal policy, new rules can be ascertained to improve the basic control strategy. The resulting new control strategy is shown to achieve better fuel economy through simulations on a detailed vehicle model.

Method and apparatus for adaptive hybrid vehicle control

Abstract: A method and apparatus for controlling a hybrid vehicle having an auxiliary power unit, at least one energy storage device, at least one electric drive motor for traction, and a controller with associated memory. The method initially involves the steps of acquiring data for the current vehicle operating state for a variable control interval and storing the vehicle operating state data as measured operating state variables. Simulated vehicle operating state data is generated by inputting the measured vehicle operating state variables into a simulation model running on-board in the controller memory. The simulation model is validated for the control interval by comparing simulated vehicle response data generated by the simulation model with corresponding measured operating state variables. The measured operating state data is analyzed to predict the vehicle operating state for the next control interval, and a control scheme is generated for optimizing energy management of the auxiliary power unit, the at least one energy storage device and the at least one electric drive motor for the predicted operating state by running the simulation model through various iterations and monitoring the simulated vehicle response data to select the optimal control scheme for the next control interval. Finally, the auxiliary power unit, the at least one energy storage device and the at least one electric drive motor are controlled through the controller according to the optimal control scheme for the next control interval. The control method of the present invention adapts to changing driving conditions and component parameter changes.

On the coupling between the plant and controller optimization problems

Abstract: Examines plant and controller optimization problems. One can solve these problems sequentially, iteratively, using a nested (or bi-level) strategy, or simultaneously. Unlike the nested and simultaneous strategies, the sequential and iterative strategies fail to guarantee system-level optimality. This is because the plant and controller optimization problems are coupled. This coupling is introduced using a simple experiment. To prove it theoretically, the necessary conditions for combined plant and controller optimality are derived. These combined optimality conditions differ from the individual sets of necessary conditions for plant and controller optimality by a coupling term that reflects the plant design's influence on the plant dynamics and control input constraints.

Evolutionary algorithms and their application to optimal control studies

Abstract: Coherent control of a physical or chemical process can be achieved by using phase and amplitude modulated femtosecond laser pulses. A self-learning loop, which connects a femtosecond pulse shaper, an optimization algorithm, and an experimental feedback signal, can automatically steer the interaction between system and electric field and allows control even without any knowledge of the Hamiltonian. The dependability of such a loop is essential to the significance of the optimization results, assigning the optimization algorithm an important role within these learning loops. In this paper, an evolutionary strategy is presented in detail that has successfully been applied to femtosecond pulse shaping in optimal control experiments. A general introduction to evolutionary algorithms is given and the specific adaptation for femtosecond pulse shaping is described. The stability and effectiveness of the algorithm is investigated both in experiments and simulations with an emphasis on the influence of steering parameters of the algorithm, number of configurations in search space, and noise. The algorithm optimizes a set of variables parametrizing the electric field. This particular mapping greatly facilitates the dissection of the optimization goal which is demonstrated by three possible parametrizations and associated applications: polynomial phase functions and adaptive femtosecond pulse compression, periodic phase functions and control of nonlinear photon transitions, multiple pulse structures and control of molecular dynamics.

Event-driven power management

Abstract: Energy consumption of electronic devices has become a serious concern in recent years. Power management (PM) algorithms aim at reducing energy consumption at the system-level by selectively placing components into low-power states. Formerly, two classes of heuristic algorithms have been proposed for PM: timeout and predictive. Later, a category of algorithms based on stochastic control was proposed for PM. These algorithms guarantee optimal results as long as the system that is power managed can be modeled well with exponential distributions. We show that there is a large mismatch between measurements and simulation results if the exponential distribution is used to model all user request arrivals. We develop two new approaches that better model system behavior for general user request distributions. Our approaches are event-driven and give optimal results verified by measurements. The first approach we present is based on renewal theory. This model assumes that the decision to transition to low-power state can be made in only one state. Another method we developed is based on the time-indexed semi-Markov decision process (TISMDP) model. This model has wider applicability because it assumes that a decision to transition into a lower-power state can be made upon each event occurrence from any number of states. This model allows for transitions into low-power states from any state, but it is also more complex than our other approach. It is important to note that the results obtained by renewal model are guaranteed to match results obtained by TISMDP model, as both approaches give globally optimal solutions. We implemented our PM algorithms on two different classes of devices: two different hard disks and client-server wireless local area network systems such as the SmartBadge or a laptop. The measurement results show power savings ranging from a factor of 1.7 up to 5.0 with insignificant variation in performance.

Differential Neural Networks for Robust Nonlinear Control: Identification, State Estimation and Trajectory Tracking

Abstract: Theoretical Study: Neural Networks Structures Nonlinear System Identification: Differential Learning Sliding Mode Identification: Algebraic Learning Neural State Estimation Passivation via Neuro Control Neuro Trajectory Tracking Neurocontrol Applications: Neural Control for Chaos Neuro Control for Robot Manipulators Identification of Chemical Processes Neuro Control for Distillation Column General Conclusions and Future Work Appendices: Some Useful Mathematical Facts Elements of Qualitative Theory of ODE Locally Optimal Control and Optimization.

Second Order Methods for Optimal Control of Time-Dependent Fluid Flow

Abstract: Second order methods for open loop optimal control problems governed by the two-dimensional instationary Navier--Stokes equations are investigated Optimality systems based on a Lagrangian formulation and adjoint equations are derived The Newton and quasi-Newton methods as well as various variants of SQP methods are developed for applications to optimal flow control, and their complexity in terms of system solves is discussed Local convergence and rate of convergence are proved A numerical example illustrates the feasibility of solving optimal control problems for two-dimensional instationary Navier--Stokes equations by second order numerical methods in a standard workstation environment

Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

Abstract: The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in finite time horizon. Examples are presented to illustrate the results established.

Naive control of the double integrator

Abstract: We deal with a form of controller evaluation that may be called naive control In naive control, a control algorithm derived under nominal (or ideal) conditions is evaluated by analytical or numerical means under off-nominal (or nonideal) conditions that were not assumed in the formal synthesis procedure Under such nonideal conditions, the controller may or may not perform well This approach is distinct from robust control, which seeks to accommodate off-nominal perturbations in the synthesis procedure We consider the double integrator plant, which is one of the most fundamental systems in control applications, representing single degree-of-freedom translational and rotational motion Applications of the double integrator include low-friction, free rigid-body motion, such as single-axis spacecraft rotation and rotary crane motion The double integrator plant considered includes a saturation nonlinearity on the control input

Optimal preview car steering control

Abstract: Steering of a car to follow a prescribed path with minimal error is represented as a problem in optimal linear discrete time preview control. A standard yaw/sideslip linear car model is put into discrete time form and joined with a road preview model. A quadratic cost function consisting of terms describing path and attitude errors with respect to a roadway and steering angle control is minimised by standard optimal control theory methods, using MATLAB to perform the necessary computations. The form taken by the optimal preview control, with variations in the weighting of terms in the cost function and with variations in the vehicle speed, is established. The results are examined in the context of real driving and tested by simulation of manoeuvres using the optimal steering control in what is thought to approximate the manner of a real driver. New insights into steering of vehicles are generated and new avenues for exploration of the influences on the driver of varying the vehicle dynamic properties are opened up.