Discrete-time decentralized optimal controllers for multimachine power systems

Decentralized compensation of large-scale power systems has the appealing feature that local substations may be controlled by a small subset of state or output variables. In this paper, the problem of decentralized control by discrete-time compensation is addressed. By formulating the dynamics of each subsystem and including the interaction terms with other subsystems, a performance measure is constructed, based upon local desired system performance. This resulting controller is optimal, even if the subsystems are strongly coupled. An example using a 10-machine power system is provided to illustrate the improvement of the system response to faults when compared to classical excitation control.     

Genetic algorithms for designing loop layout manufacturing systems

A common layout for flexible manufacturing system is loop network with machines arranged in a cycle and materials transported in only one direction around the cycle. Congestion is a common measure for evaluating a loop layout. This paper investigates the problem of designing loop layout system with both of minsum and minmax congestion measures. A hybrid heuristic of genetic algorithms and neighborhood search is developed for solving such problem and preliminary computational results are reported.     

Deadbeat algorithms for output controllers in discrete-time multivariable systems

This paper studies the problem of designing output deadbeat controllers to force the state of discrete-time multivariable systems to zero in a finite number of samples. Two algorithms are considered. The first is based on the fact that the closed-loop eigenstructure assignable by output feedback is constrained by the requirement that the left and right eigenvectors must be in certain subspaces. In the second algorithm, the output gain matrix is computed through the optimization of certain parameters of the controller, while maintaining its structural constraints. Computer programs have been developed to realize the two algorithms and examples are given to illustrate the feasibility of the techniques.     

Design of optimal disturbance rejection PID controllers usinggenetic algorithms

This paper presents a method to design an optimal disturbance rejection PID controller. First, a condition for disturbance rejection of a control system-H_∞-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     

A probabilistic approach for designing nonlinear optimal robust tracking controllers for unmanned aerial vehicles

In this study, we propose a probabilistic approach for designing nonlinear optimal robust tracking controllers for unmanned aerial vehicles. The controller design is formulated in terms of a multi-objective optimization problem that is solved by using a bio-inspired optimization algorithm, offering high likelihood of finding an optimal or near-optimal global solution. The process of tuning the controller minimizes differences between system outputs and optimal specifications given in terms of rising time, overshoot and steady-state error, and the controller succeed in fitting the performance requirements even considering parametric uncertainties and the nonlinearities of the aircraft. The stability of the controller is proved for the nominal case and its robustness is carefully verified by means of Monte Carlo simulations.     

Exploiting timed automata based fuzzy controllers for designing adaptive intrusion detection systems

Network intrusion detection systems (NIDSs) are pattern recognition problems that classify network traffic patterns as either ‘normal’ or ‘abnormal’. Precisely, the main aim of intrusion detection is to identify unauthorized use, misuse, and abuse of computers by detecting malicious network activities such as port scans, denial of service or other attempts to crack computer network environments. Even though the incorporation of conventional Soft Computing techniques in NIDSs has yielded to good solutions, the strong dynamism characterizing network intrusion patterns tend to invalidate the usability of existing framework. To tackle this issue, our proposal performs an adaptive supervised learning on a collection of time series that characterizes the network behavior to create a so-called timed automata-based fuzzy controller (TAFC), i.e. an evolvable fuzzy controller whose dynamic features allow to design an advanced network intrusion detection system able to directly deal with computer network dynamism and support networks’ administrators to prevent eventual damages coming from unauthorized network intrusion. As will be shown in experiments, where our approach has been compared with a conventional Mamdani fuzzy controller, the proposed system reduces the detection error and, as consequence, improves the computer network robustness.     

Locally optimal controllers and globally inverse optimal controllers

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing an LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem.     

Synthesis of optimal controllers for piecewise affine systems with sampled-data switching

This paper discusses the optimal control problem of the continuous-time piecewise affine (PWA) systems with sampled-data switching, where the switching action is executed based upon a condition on the state at each sampling time. First, an algebraic characterization for the problem to be feasible is derived. Next, an optimal continuous-time controller is derived for a general class of PWA systems with sampled-data switching, for which the optimal control problem is feasible but whose subsystems in some modes may be uncontrollable in the usual sense. Finally, as an application of the proposed approach, the high-speed and energy-saving control problem of the CPU processing is formulated, and the validity of the proposed methods is shown by numerical simulations.     

Compensating for computational delay in digital equivalent ofcontinuous control systems

A computer-aided method to compensate for the computational delay in the digital equivalent of continuous control systems is presented. The objective is to obtain the transfer function of the digital controller so that the performance of the equivalent digital control system is as close to that of the existing continuous system as possible. This is done by matching the frequency response of the digital control system to that of the existing system with a minimum weighted mean-square error. A formula for computing the parameters of the digital controller is obtained as a result. The design method is illustrated with an example     

Escalator method for determining optimal state feedback controllers for bordered unconstrained bilinear systems

A method is presented for obtaining the optimal quadratic state feedback control law of a bordered bilinear system in terms of the optimal control law of the system before bordering. The method is based on the Cholesky factorization of the system matrix which is assumed to be symmetric and positive definite. Under a certain condition on the norm of the bordering vector a simple closed-form expression for the stabilizing state feedback gain matrix is obtained.     

Design of optimal controllers for spatially invariant systems with finite communication speed

We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which all spatially invariant systems with this property can be characterized. After establishing the closure of such systems under linear fractional transformations, we formulate the H₂ optimal control problem using the model-matching framework. We demonstrate that, even though the optimal control problem is non-convex with respect to some state-space design parameters, a variety of numerical optimization algorithms can be employed to relax the original problem, thereby rendering suboptimal controllers. In particular, for the case in which every subsystem has scalar input disturbance, scalar measurement, and scalar actuation signal, we investigate the application of the Steiglitz–McBride, Gauss–Newton, and Newton iterative schemes to the optimal distributed controller design problem. We apply this framework to examples previously considered in the literature to demonstrate that, by designing structured controllers with infinite impulse response, superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree.     

Synthesis of minimax optimal controllers for uncertain time-delay systems with structured uncertainty

This paper is concerned with the design of robust state feedback controllers for a class of uncertain time-delay systems. The uncertainty is assumed to satisfy a certain integral quadratic constraint. The controller proposed is a minimax optimal controller in the sense that it minimizes the maximum value of a corresponding linear quadratic cost function over all admissible uncertainties. The controller leads to an absolutely stable closed loop uncertain system and is constructed by solving a finite dimensional parameter-dependent algebraic Riccati equation.     

Recurrent fuzzy network design using hybrid evolutionary learning algorithms

This paper proposes a recurrent fuzzy network design using the hybridization of a multigroup genetic algorithm and particle swarm optimization (R-MGAPSO). The recurrent fuzzy network designed here is the Takagi–Sugeno–Kang (TSK)-type recurrent fuzzy network (TRFN), in which each fuzzy rule comprises spatial and temporal sub-rules. Both the number of fuzzy rules and the parameters in a TRFN are designed simultaneously by R-MGAPSO. In R-MGAPSO, the techniques of variable-length individuals and the local version of particle swarm optimization are incorporated into a genetic algorithm, where individuals with the same length constitute the same group, and there are multigroups in a population. Population evolution consists of three major operations: elite enhancement by particle swarm optimization, sub-rule alignment-based crossover, and mutation. To verify the performance of R-MGAPSO, dynamic plant and a continuous-stirred tank reactor controls are simulated. R-MGAPSO performance is also compared with genetic algorithms in these simulations.     

Finite-dimensional optimal controllers for nonlinear plants

Optimal risk sensitive feedback controllers are now available for very general stochastic nonlinear plants and performance indices. They consist of nonlinear static feedback of so called information states from an information state filter. In general, these filters are linear, but infinite dimensional, and the information state feedback gains are derived from (doubly) infinite dimensional dynamic programming. The challenge is to achieve optimal finite dimensional controllers using finite dimensional calculations for practical implementation.This paper derives risk sensitive optimality results for finite-dimensional controllers. The controllers can be conveniently derived for ‘linearized’ (approximate) models (applied to nonlinear stochastic systems). Performance indices for which the controllers are optimal for the nonlinear plants are revealed. That is, inverse risk-sensitive optimal control results for nonlinear stochastic systems with finite dimensional linear controllers are generated. It is instructive to see from these results that as the nonlinear plants approach linearity, the risk sensitive finite dimensional controllers designed using linearized plant models and risk sensitive indices with quadratic cost kernels, are optimal for a risk sensitive cost index which approaches one with a quadratic cost kernel. Also even far from plant linearity, as the linearized model noise variance becomes suitably large, the index optimized is dominated by terms which can have an interesting and practical interpretation.Limiting versions of the results as the noise variances approach zero apply in a purely deterministic nonlinear H_∞ setting. Risk neutral and continuous-time results are summarized.More general indices than risk sensitive indices are introduced with the view to giving useful inverse optimal control results in non-Gaussian noise environments.     

Internal-model-based design of repetitive and iterative learning controllers for linear multivariable systems

Repetitive and iterative learning control are two modern control strategies for tracking systems in which the signals are periodic in nature. This paper discusses repetitive and iterative learning control from an internal model principle point of view. This allows the formulation of existence conditions for multivariable implementations of repetitive and learning control. It is shown that repetitive control can be realized by an implementation of a robust servomechanism controller that uses the appropriate internal model for periodic distrubances. The design of such controllers is discussed. Next it is shown that iterative learning control can be implemented in the format of a disturbance observer/compensator. It is shown that the resulting control structure is dual to the repetitive controller, and that both constitute an implementation of the internal model principle. Consequently, the analysis and design of repetitive and iterative learning control can be generalized to the powerful analysis and design procedure of the internal model framework, allowing to trade-off the convergence speed for periodic-disturbance cancellation versus other control objectives, such as stochastic disturbance suppression.     

Compensatory neurofuzzy systems with fast learning algorithms

In this paper, a new adaptive fuzzy reasoning method using compensatory fuzzy operators is proposed to make a fuzzy logic system more adaptive and more effective. Such a compensatory fuzzy logic system is proved to be a universal approximator. The compensatory neural fuzzy networks built by both control-oriented fuzzy neurons and decision-oriented fuzzy neurons cannot only adaptively adjust fuzzy membership functions but also dynamically optimize the adaptive fuzzy reasoning by using a compensatory learning algorithm. The simulation results of a cart-pole balancing system and nonlinear system modeling have shown that: 1) the compensatory neurofuzzy system can effectively learn commonly used fuzzy IF-THEN rules from either well-defined initial data or ill-defined data; 2) the convergence speed of the compensatory learning algorithm is faster than that of the conventional backpropagation algorithm; and 3) the efficiency of the compensatory learning algorithm can be improved by choosing an appropriate compensatory degree.     

Trigonometric approximation of optimal periodic control problemsfor systems with inertial controllers

A constrained optimal periodic control (OPC) problem for nonlinear systems with inertial controllers is considered. A sequence of approximate problems containing trigonometric polynomials for approximation of the state, control, and functions in the state equations and in the optimality criterion is formulated. Sufficient conditions for a sequence of nearly optimal solutions of approximate problems to be norm-convergent to the basic problem optimal solution are derived. It is pointed out that the direct approximation approach in the space of state and control combined with the finite-dimensional optimization methods such as the space covering and gradient-type methods makes probable the finding of the global optimum for OPC problems     

Improved algorithms for optimal length resolution refutation in difference constraint systems

This paper is concerned with the design and analysis of improved algorithms for determining the optimal length resolution refutation (OLRR) of a system of difference constraints over an integral domain. The problem of finding short explanations for unsatisfiable Difference Constraint Systems (DCS) finds applications in a number of design domains including program verification, proof theory, real-time scheduling, and operations research. These explanations have also been called “certificates” and “refutations” in the literature. This problem was first studied in Subramani (J Autom Reason 43(2):121–137, 2009), wherein the first polynomial time algorithm was proposed. In this paper, we propose two new strongly polynomial algorithms which improve on the existing time bound. Our first algorithm, which we call the edge progression approach, runs in O(n ² · k + m · n · k) time, while our second algorithm, which we call the edge relaxation approach, runs in O(m · n · k) time, where m is the number of constraints in the DCS, n is the number of program variables, and k denotes the length of the shortest refutation. We conducted an extensive empirical analysis of the three OLRR algorithms discussed in this paper. Our experiments indicate that in the case of sparse graphs, the new algorithms discussed in this paper are superior to the algorithm in Subramani (J Autom Reason 43(2):121–137, 2009). Likewise, in the case of dense graphs, the approach in Subramani (J Autom Reason 43(2):121–137, 2009) is superior to the algorithms described in this paper. One surprising observation is the superiority of the edge relaxation algorithm over the edge progression algorithm in all cases, although both algorithms have the same asymptotic time complexity.     

Algorithms for constructing optimal controllers for gaslift operation

We consider the optimal stabilization problem for delivered gas and gaslift operation debit for oil wells. Under certain natural assumptions, the general problem reduces to a linear-quadratic control problem that lets us find program controls and trajectories on which we further construct the optimal controller with respect to all phase coordinates and a (debit) part of them in both continuous and discrete case. For a special case, numerical results are illustrated with graphs that let us use this method in oilfield practice.