Difficult Control Problem Research Articles

Improved sample complexity estimates for statistical learning control of uncertain systems

Probabilistic methods and statistical learning theory have been shown to provide approximate solutions to difficult control problems. Unfortunately, the number of samples required in order to guarantee stringent performance levels may be prohibitively large. This paper introduces bootstrap learning methods and the concept of stopping times to drastically reduce the bound on the number of samples required to achieve a performance level. We then apply these results to obtain more efficient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems.

Application of Wiener model predictive control (WMPC) to an industrial C2-splitter

Dual composition control of a high-purity distillation column is recognized as an industrially important, yet notoriously difficult control problem. It is proposed, however, that Wiener models, consisting of a linear dynamic element followed in series by a static nonlinear element, are ideal for representing this and several other nonlinear processes. They are relatively simple models requiring little more effort in development than a standard linear step response model, yet offer superior characterization of systems with highly nonlinear gains. Wiener models may be incorporated into MPC schemes in a unique way that effectively removes the nonlinearity from the control problem, preserving many of the favorable properties of linear MPC, especially in the analysis of stability. In this paper, Wiener model predictive control is applied to an industrial C2-splitter at the Orica Olefines plant with promising results.

Advanced Geno-Fuzzy Techniques for Drum Level Control in Thermal Power Plants

The evolution of boiler control systems has followed directly from the evolution of electronics and microprocessor technologies over the last fifteen years. There has been much interest lately in the so-called intelligent control systems, which can dynamically learn and make decisions. They have the ability to react in a successful manner to a variety of uncertainties. The aim of this paper is to investigate possible use of advanced hybrid geno-fuzzy techniques for boiler control in thermal power plants. The problem addressed here is the drum level control, a difficult control problem.

Application of Wiener model predictive control (WMPC) to a pH neutralization experiment

pH control is recognized as an industrially important, yet notoriously difficult control problem. Wiener models, consisting of a linear dynamic element followed in series by a static nonlinear element, are considered to be ideal for representing this and several other nonlinear processes. Wiener models require little more effort in development than a standard linear step-response model, yet offer superior characterization of systems with highly nonlinear gains. These models may be incorporated into model predictive control (MPC) schemes in a unique way which effectively removes the nonlinearity from the control problem, preserving many of the favorable properties of linear MPC. In this paper, Wiener model predictive control (WMPC) is evaluated experimentally, and also compared with benchmark proportional integral derivative (PID) and linear MPC strategies, considering the effects of output constraints and modeling error.

Dynamic neural controllers for induction motor

The paper reports application of recently developed adaptive control techniques based on neural networks to the induction motor control. This case study represents one of the more difficult control problems due to the complex, nonlinear, and time-varying dynamics of the motor and unavailability of full-state measurements. A partial solution is first presented based on a single input-single output (SISO) algorithm employing static multilayer perceptron (MLP) networks. A novel technique is subsequently described which is based on a recurrent neural network employed as a dynamical model of the plant. Recent stability results for this algorithm are reported. The technique is applied to multiinput-multioutput (MIMO) control of the motor. A simulation study of both methods is presented. It is argued that appropriately structured recurrent neural networks can provide conveniently parameterized dynamic models for many nonlinear systems for use in adaptive control.

Concave Programming in Control Theory

We show in the present paper that many open and challenging problems in control theory belong the the class of concave minimization programs. More precisely, these problems can be recast as the minimization of a concave objective function over convex LMI (Linear Matrix Inequality) constraints. As concave programming is the best studied class of problems in global optimization, several concave programs such as simplicial and conical partitioning algorithms can be used for the resolution. Moreover, these global techniques can be combined with a local Frank and Wolfe feasible direction algorithm and improved by the use of specialized stopping criteria, hence reducing the overall computational overhead. In this respect, the proposed hybrid optimization scheme can be considered as a new line of attack for solving hard control problems. Computational experiments indicate the viability of our algorithms, and that in the worst case they require the solution of a few LMI programs. Power and efficiency of the algorithms are demonstrated for a realistic inverted-pendulum control problem. Overall, this dedication reflects the key role that concavity and LMIs play in difficult control problems.

Rollout Algorithms for Stochastic Scheduling Problems

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.

Computational method based on state parametrization for solving constrained nonlinear optimal control problems

In this paper, we present a method for solving nonlinear optimal control problems subject to terminal state constraints and control saturation constraints. This method is based on using the quasilinearization and the state variables parametrization by using Chebyshev polynomials. In this method, there is no need to integrate the system state equations or the costate equations. By virtue of the quasilinearization and the state parametrization, the difficult constrained nonlinear optimal control problem is approximated by a sequence of small quadratic programming problems which can be solved easily. To show the effectiveness of the proposed method, the simulation results of a numerical example are shown.

Maximizing productivity of a continuous fermenter using nonlinear adaptive optimizing control

The control of a continuously operated fermenter at its maximum productivity level gives rise to a difficult control problem as the location of the optimum operating point changes due to the disturbances. In addition, the fermenter exhibits a change in the sign of the steady state gain near the optimum operating point. This study is aimed at developing an on-line optimizing control scheme that can track the changing location of the steady state optimum so as to maximize the fermenter productivity. A nonlinear Laguerre model, whose parameters are estimated on-line, is used for tracking the optimum operating point. The control at the optimum point is achieved using an adaptive nonlinear MPC strategy that uses the nonlinear Laguerre model for prediction. The efficiency of the proposed algorithm is demonstrated by simulating the control of a continuous fermenter that exhibits shift in the location of the optimum operating point in response to the changes in the maximum specific growth rate. The proposed on-line optimizing control strategy is shown to result in a considerable improvement in the closed loop performance even in the presence of measurement noise.

Industrial Practice of Soft Sensor Based Predictive Control in Fluid Catalytic Cracking Processes

The operation of Fluid Catalytic Cracking (FCC) processes exhibits strongly nonlinear and highly interactive dynamic behavior as well as having poorly understood reaction kinetics with many unmeasured operating variables which can play a key role in determining performance and give rise to difficult control problems. Soft sensors, which use easily measured and continuously available temperature, pressure and flowrate measurements along with system models which make use of conservation equations to assimilate on-line learning parameters are essential for advanced control. This article reports the application of a predictive control strategy using a soft sensor on an existing industrial FCC unit.

Soft Sensor Based Predictive Control of Industrial Fluid Catalytic Cracking Processes

The operation of Fluid Catalytic Cracking (FCC) processes exhibits strongly nonlinear and highly interactive dynamic behaviour as well as having poorly understood reaction kinetics with many unmeasured operating variables which can play key roles in determining performance and give rise to difficult control problems. Soft sensors, which use easily measured and continuously available temperature, pressure and flowrate measurements, along with system models which make use of conservation equations to assimilate on-line learning parameters, are essential for advanced control. This article reports the application of a predictive control strategy using two soft sensors on an existing industrial FCC process. Both approaches resulted in improvements using this approach and the general issues are discussed in terms of generic procedures.

Neural and Neurofuzzy FELA Adaptive Robot Control Using Feedforward and Counterpropagation Networks

In this paper, the application of neural networks and neurofuzzy systems to the control of robotic manipulators is examined. Two main control structures are presented in a comparative manner. The first is a Counter Propagation Network-based Fuzzy Controller (CPN-FC) which is able to self-organize and correct on-line its rule base. The self-tuning capability of the fuzzy logic controller is attained by taking advantage of the structural equivalence between the fuzzy logic controller and a counterpropagation network. The second control structure is a more familiar neural adaptive controller based on a feedforward (MLP) network. The neural controller learns the inverse dynamics of the robot joints, and gradually eliminates the model uncertainties and disturbances. Both schemes cooperate with the computed torque control algorithm, and in that way the reduction of their complexity is achieved. The ability of adaptive fuzzy systems to compete with neural networks in difficult control problems is demonstrated. A sufficient set of numerical results is included.

Truck Backer-Upper Control Using Adaptive Critic Learning

Backing up a truck to a loading dock is a difficult nonlinear control problem. Interesting applications of backpropagation (BP) learning to solve this problem have been proposed. However, BP requires extensive training. In this paper, we propose a solution based on the adaptive critic learning. The proposed scheme is considered as a first attempt towards solving Truck Backer-Upper (TBU) using this kind of learning. Results obtained through computer simulation of TBU are presented.

General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators

Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, "Are TS fuzzy systems with linear rule consequent universal approximators?" If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided.

Nonlinear internal model control using quadratic prediction models

This study is aimed at development of a nonlinear IMC controller that can handle a larger class of nonlinear systems than hitherto, including the singular systems that exhibit change in the sign of the steady state gain. The construction of the model inverse is achieved through inversion of successive quadratic approximation of the nonlinear model operator. The controller synthesis problem is formulated as minimization of 2-norm of single step prediction error. Using the theory of solutions of the multidimensional quadratic equations, a closed form dead-beat type quadratic control law is evolved. The performance of the proposed control law is demonstrated by simulating control of two highly nonlinear systems and also a singular system. In the case of singular system, it has been shown that the proposed quadratic control law can be effectively used for handling a difficult robust control problem arising out of non-attainability of set point due to plant-model mismatch.

Positioning of the Two-link Arm by Manual Control.

The problem-solving ability of a human in manual control is considered. The purpose of the manual control is the positioning of the two-link arm with a free joint. This kind of manipulator are getting popular recently because of its simplicity. The control of the manipulator, however, is difficult because the motion is governed by a set of nonlinear equations. A real-time simulator is used to perform the experiment of manual control. It is concluded that a human can find some satisfactory control patterns after enough training. These results are interesting from the theoretical point of view, they suggest a possible theoretical approach to this difficult control problem.

Forming Neural Networks Through Efficient and Adaptive Coevolution

This article demonstrates the advantages of a cooperative, coevolutionary search in difficult control problems. The symbiotic adaptive neuroevolution (SANE) system coevolves a population of neurons that cooperate to form a functioning neural network. In this process, neurons assume different but overlapping roles, resulting in a robust encoding of control behavior. SANE is shown to be more efficient and more adaptive and to maintain higher levels of diversity than the more common network-based population approaches. Further empirical studies illustrate the emergent neuron specializations and the different roles the neurons assume in the population.

Unconstrained and Constrained Model Predictive Control using Wiener Models: An Application to pH Neutralization

pH control is recognized as an industrially important, yet notoriously difficult control problem. It is proposed, however, that Wiener models, consisting of a linear dynamic element followed in series by a static nonlinear element, are ideal for representing this and several other nonlinear processes. They are relatively simple models, requiring little more effort in development than a standard linear step response model, yet offer superior characterization of systems with highly nonlinear gains. In this paper Wiener model predictive control is compared experimentally to both PID and linear MPC, with the effects of output constraints and modeling error also being considered.

Genetic algorithm for control design of biped locomotion

Dynamic biped walking is a difficult control problem. The design involves that of the controller as well as the gait. A typical design procedure involves tedious analysis, careful planning, and testing. The procedure is time consuming and the analysis is often based on some linearized model. Selection of control parameters and nominal trajectory determines the quality of control and in typical designs, some or all of the parameters are selected intuitively. The result is often not the best. If some special goal (such as to walk as fast as possible) is desirable, the design may become even harder. While the analytical approach is not easy, one possible alternative is to obtain the optimal or near-optimal design through parameter search. This study explores this approach. The design of the biped controller and gait is formulated as a parameter search problem, and a genetic algorithm is applied to help obtain the optimal design. Designs to achieve different goals, such as being able to walk on an inclined surface, walk at a high speed, or walk with a specified step size have been evolved with the use of the genetic algorithm. Simulation results show that the genetic algorithm (GA) is capable of finding good solutions. © 1997 John Wiley & Sons, Inc.

Control of Chemical Reactors Using Multiple-Model Adaptive Control (MMAC)

Multiple-Model Adaptive Control (MMAC) is shown to be an effective strategy for controlling nonlinear chemical processes. In this paper, MMAC is applied to two difficult control problems that may be encountered in continuous stirred tank reactors (CSTRs). In the first example, product concentration is controlled in an isothermal CSTR exhibiting input multiplicities and nonminimum phase behavior (Van de Vusse reaction). The MMAC configuration provides disturbance rejection where a fixed-parameter PID controller fails. The second example involves temperature control of a CSTR which has output multiplicities. While a single PID controller can stabilize the plant over a large operating range, its performance can be quite poor since the plant dynamics vary widely. MMAC is shown to give significantly better performance when moving from the open-loop stable regions to the open-loop unstable operating region.