Optimal Control Synthesis Research Articles

Partial-State Stabilization and Optimal Feedback Control for Stochastic Dynamical Systems

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial-state stabilization of stochastic dynamical systems. Partial asymptotic stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation, and hence, guaranteeing both partial stability in probability and optimality. The overall framework provides the foundation for extending optimal linear-quadratic stochastic controller synthesis to nonlinear-nonquadratic optimal partial-state stochastic stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time-varying stochastic systems with quadratic and nonlinear-nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine stochastic nonlinear systems using an inverse optimality framework tailored to the partial-state stochastic stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion.

H∞ Optimal Controller Design With Closed-Loop Positive Real Constraints

Positive real constraints on the closed-loop of linear systems guarantee stable interaction with arbitrary passive environments. Two such methods of H∞ optimal controller synthesis subject to a positive real constraint are presented and demonstrated on numerical examples. The first approach is based on an established multi-objective optimal control framework using linear matrix inequalities and is shown to be overly restrictive and ultimately infeasible. The second method employs a sector transformation to substitute the positive real constraint with an equivalent H∞ constraint. In two examples, this method is shown to be more reliable and displays little change in the achieved H∞ norm compared to the unconstrained design, making it a promising tool for passivity-based controller design.

Synthesis of Optimal Efforts Control in Electromechanical Systems with Elastic Mechanical Links

The article presents a solution, in optimal statement, of a problem of efforts control synthesis in elastic mechanisms which comprises significant forces of friction and inertia. Different methods of optimum control of electromechanical systems were compared, and the applicability of the methods based on variations calculus was proved. The application of the integral control quality criterion allowed determining the rational structure and parameters of a force regulator in elastic elements of mechanisms, during the operation in the conditions of uncertain perturbation actions. During the synthesis of the optimum effort regulator, real limitations were considered which are attached to the control impact and the conditions assuring stability of a control system with the synthesized regulator to possible changes of parameters of a controlled object are defined. The performed studies demonstrated the effectiveness of the synthesized force regulator in electromechanical systems with elastic gears in the case of changes in perturbation actions. The proposed method for the synthesis of the optimal effort regulator in elastic mechanisms was applied during the creation of the training simulator “Exit 2”, which was designed to train astronauts to work in zero gravity conditions, and during the modification of MP100 balanced type manipulators with 100 kg load-carrying capability.

Synthesis of optimal boundary control of parabolic systems with delay and distributed parameters on the graph

Synthesis of optimal boundary control of parabolic systems with delay and distributed parameters on the graph

Optimal Control Synthesis for Stochastic Dynamical Systems of Random Structure with the Markovian Switchings

Optimal Control Synthesis for Stochastic Dynamical Systems of Random Structure with the Markovian Switchings

FEM model-based optimal control synthesis for curing a large composite structure with CAD imported geometry

The paper studies a problem of optimal control synthesis for curing a large composite structure using open die moulding in an autoclave. The necessary control should eliminate early hard skin formation, emergence of resin-rich or resin-dry areas, insufficient consolidation, and uneven cure. This purpose is achieved through providing uniform distribution of degree of cure and temperature within the cured part volume. The used approach is illustrated on the example of the large CFRP aircraft panel manufactured by means of two-stage curing cycle. The forward problem combines the heat transfer and autocatalytic kinetic equations, which are linked by the specific heat capacity, thermal conductivity coefficient and by the exothermal heat source that depend on the prepreg’s degree of cure. The control synthesis problem is formulated as a multi-objective optimization problem where minimized objectives are deviations of temperature and degree of cure within a cured part, considering constraints imposed by thermal-kinetic properties of prepreg and manufacturing requirements. The Pareto-based optimization algorithm, which executes the mapping of a subset of design space to the objectives space by the cyclic calling the forward problem implemented as a finite element model, allows estimating the best achievable quality indicators of manufactured composite parts, finding satisfactory parameters of the control law, and decision-making considering all imposed constraints.

Optimal perimeter control synthesis for two urban regions with aggregate boundary queue dynamics

Perimeter control policies for urban regions with Macroscopic Fundamental Diagram (MFD) modeling have been presented in previous works. The control policies might meter the number of transferring vehicles from one region to another, resulting in queueing vehicles at regional boundaries. Concentrated vehicles at boundaries might affect the existence of well-defined MFDs. Most previous works neglect the effect of the boundary concentrated vehicles on the traffic flow dynamics, and do not explicitly consider their effect on the perimeter control policy.This paper introduces a new MFD-based model for two-region networks with aggregate boundary queue dynamics. The dynamic flow characteristics for the two urban regions are modeled by the MFD functions, while aggregate boundary queue dynamics for both regions are modeled by input-output balance differential equations. Maximum lengths are imposed on the aggregate boundary queues, that aim at maintaining the existence of well-defined MFDs and their dynamics.Based on the developed model, the optimal control policy to maximize the total network throughput is found. Analytical solutions for the optimal perimeter control problem, with constrained perimeter control inputs and constrained lengths of aggregate boundary queues, are derived. The optimal synthesis for principal cases are found and verified by numerical tests. The numerical results demonstrate the effect of aggregate boundary queues on the optimal perimeter control policy.

Quantum Linear Systems Theory

This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). Such sys- tems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or ap- proximated by linear QSDEs include interconnections of optical cavities, beam-spitters, phase-shifters, optical parametric am- plifiers, optical squeezers, and cavity quantum electrodynamic systems. With advances in quantum technology, the feedback control of such quantum systems is generating new challenges in the field of control theory. Potential applications of such quantum feedback control systems include quantum computing, quantum error correction, quantum communications, gravity wave detection, metrology, atom lasers, and superconducting quantum circuits. A recently emerging approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient imple- mentation. This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case. An important issue which arises both in the modelling of linear quantum systems and in the synthesis of linear coherent quantum controllers is the issue of physical realizability. This issue relates to the property of whether a given set of QSDEs corresponds to a physical quantum system satisfying the laws of quantum mechanics. The paper will cover recent results relating the question of physical realizability to notions occuring in linear systems theory such as lossless bounded real systems and dual J-J unitary systems.

Quadratic Optimal Control of Aerodynamic Vectored UAV at High Angle of Attack

Small-scale Unmanned Air Vehicles (UAVs) belong to the class of less than one meter box dimension and are widely used in different civilian and military roles. In this paper, quadratic optimal control synthesis is carried out on a rigid-wing UAV at low speeds with improved aerodynamic performance. The aircraft is equipped with a unique feature of ‘aerodynamic vectoring’ such that the angle of incidence of the wing is dealt as an independent control variable. The aircraft motion is studied in longitudinal plane. More specifically, controller is designed using Linear Quadratic Regulation (LQR) and Linear Quadratic Gaussian (LQG) formulations which are carried out for two configurations – fixed-wing UAV and ‘Aerodynamic Vectored’ UAV. The control architecture shows avoidance of instabilities associated with short period and phugoid modes. Moreover, aerodynamic vectored UAV manifests better performance in terms of stability, control effort, settling time and overshoot.

STATIC OUTPUT FEEDBACK CONTROL OF STOCHASTIC DECENTRALIZED SINGULARLY PERTURBED SYSTEMS

Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an output feedback controller by standard stochastic control theory techniques using Linear Quadratic Regulator (LQR) approach and minimizing a Hamiltonian function with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Discretization for Sampled-Data Controller Synthesis via Piecewise Linear Approximation

This paper develops a new discretization method with piecewise linear approximation for the $L_{1}$ optimal controller synthesis problem of sampled-data systems, which is the problem of minimizing the $L_{\infty}$ -induced norm of sampled-data systems. We apply fast-lifting on the top of the lifting technique, by which the sampling interval $[0,h)$ is divided into $M$ subintervals with an equal width. The signals on each subinterval are then approximated by linear functions by introducing two types of ‘linearizing operators’ for input and output, which leads to piecewise linear approximation of sampled-data systems. By using the arguments of preadjoint operators, we provide an important inequality that forms a theoretical basis for tackling the $L_{1}$ optimal controller synthesis problem of sampled-data systems more efficiently than the conventional method. More precisely, a mathematical basis for the piecewise linear approximation method associated with the convergence rate is shown through this inequality, and this suggests that the piecewise linear approximation method may drastically outperform the conventional method in the $L_{1}$ optimal controller synthesis problem of sampled-data systems. We then provide a discretization procedure of sampled-data systems by which the $L_{1}$ optimal controller synthesis problem is converted to the discrete-time $l_{1}$ optimal controller synthesis problem. Finally, effectiveness of the proposed method is demonstrated through a numerical example.

Non-linear optimal fuzzy control synthesis for robust output tracking of uncertain micro-electro-mechanical systems

This paper considers the output tracking problem for micro-electro-mechanical systems (MEMS) under uncertainties and external disturbances. The robust non-linear controllers are designed by two methods. The first method consists of a backstepping strategy combined with a first-order sliding mode controller. Also, in order to reduce the chattering effect and to improve the robustness of the proposed scheme, a new variable universe fuzzy control action with an adaptive coefficient is used instead of the signum function in the switching control law. In the proposed fuzzy scheme, the centres of the output membership functions are optimized via three heuristic optimization algorithms including the artificial bee colony (ABC) algorithm, ant colony optimization (ACO) and particle swarm optimization (PSO). In the second method, a class of second-order sliding mode controller is combined with the backstepping strategy. The second controller includes the proposed optimal fuzzy controllers of the first method. The stability of the closed-loop systems in both approaches are proved via the Lyapunov stability criterion and the conditions of stabilization are provided by linear matrix inequalities (LMIs). Numerical simulations are carried out to verify the theoretical results and to demonstrate the robust performance of the proposed controller in output tracking of the time-varying reference signal.

Optimal investment strategies in a certain class of stochastic Merton’s terminal wealth problems

The paper studies the classical stochastic Merton’s terminal wealth portfolio problem without transaction costs and also some related problems which may serve as efficient benchmarks for developing relevant analytical techniques as applied to problems with transaction costs. Very few analytical solutions are available for all these types of the Merton’s problem, whereas effective applications of substantially numerical approaches are strongly restricted. Hence, even for quite narrow classes of problems, the development of analytical techniques constructing exact representations for optimal value functions and the corresponding optimal feedback controls is of great theoretical and practical importance. Despite some advancements, sufficiently simple single-input control-affine systems without state constraints and the subject of optimal control synthesis are investigated rather poorly in analytical and qualitative aspects. The present paper is devoted to an entirely analytical construction of the global optimal control synthesis in a certain class of stochastic Merton’s terminal wealth problems. A significant feature of the obtained optimal feedback controls is their capability to be interpreted naturally and adequately from a financial point of view as well as to observe a significant qualitative difference between stochastic and limiting deterministic cases.

Vibration control strategy for large‐scale structures with incomplete multi‐actuator system and neighbouring state information

The synthesis of optimal controllers for vibrational protection of large-scale structures with multiple actuation devices and partial state information is a challenging problem. In this study, the authors present a design strategy that allows computing this kind of controllers by using standard linear matrix inequality optimisation tools. To illustrate the main elements of the new approach, a five-story structure equipped with two interstory actuation devices and subjected to a seismic disturbance is considered. For this control setup, three different controllers are designed: an ideal state-feedback H 8 controller with full access to the complete state information and two static output-feedback H 8 controllers with restricted neighbouring state information. To assess the performance of the proposed controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations are conducted, using the full scale North-South El Centro 1940 seismic record as ground acceleration input. The obtained results indicate that, despite the severe information constraints, the proposed static output-feedback controllers attain a level of seismic protection that is very similar to that achieved by the ideal state-feedback controller with complete state information.

Linear quadratic optimal controller for cable-driven parallel robots

In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

SAT-Based Control of Concurrent Software for Deadlock Avoidance

We present a highly efficient boolean satisfiability (SAT) formulation for deadlock detection and avoidance in concurrent programs modeled by Gadara nets, a class of Petri nets. The SAT formulation is used in an optimal control synthesis framework based on Discrete Control Theory. We compare our method with existing methods and show a significant increase in scalability. Stress tests show that our technique is capable of synthesizing deadlock avoidance control logic in programs modeled by Gadara nets with over $10^{9}$ unsafe states.

Static output-feedback stabilization with optimal [formula omitted]-gain for positive linear systems

This paper is concerned with the static output-feedback stabilization with optimal L1-gain for positive linear systems. We aim to construct a static output-feedback controller such that the closed-loop system is positive, asymptotically stable and the L1-gain from the exogenous input to the regulated output is minimized. We show that when the control input or the measured output is a scalar, this problem can be directly solved via linear programming by adding a one dimensional search. Moreover, it is pointed out that the results can be extended to solve the L∞-optimal controller synthesis problem. Finally, several illustrative examples are given to show the effectiveness of the theoretical results.

Editorial optimal control of solar energy systems

SummaryThis special issue presents different applications of optimal control to solar energy systems. Papers focus on transitioning from theoretical to practical studies with emphasis on methodologies for the design, synthesis and application of optimal control to solar energy systems. Copyright © 2015 John Wiley & Sons, Ltd.

The optimal control software environment for a nonlinear system class via quadratic criteria

The paper presents a distributed software environment for a feedback optimal control synthesis. The control is performed by one class of nonlinear systems via quadratic criteria. This software environment is based on a special method of successive approximations. The successive approximation method convergence is guaranteed in the case of a single optimal control. The software implementation is performed by means of symbolic computation in a distributed environment.

Sufficient Optimality Conditions for Discrete Automaton Type Systems with Instantaneous Multiple Switchings

UDC 517.9 We consider a discrete system governing the operation of a dynamic automaton with memory. We establish sufficient optimality conditions for such a system and obtain equations for synthesis of optimal position control. Applications of the optimality con