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69
A Receding Horizon Generalization of Pointwise MinNorm Controllers
, 2000
"... Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the no ..."
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Cited by 33 (0 self)
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Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise minnorm, receding horizon, and optimal control. This framework is used to develop a control Lyapunov function based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuoustime receding horizon control law. The issue of implementation under discretetime sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise minnorm control are prove...
Lowauthority controller design via convex optimization
 AIAA Journal of Guidance, Control, and Dynamics
, 1999
"... In this paper we address the problem of lowauthority controller (LAC) design. The premise is that the actuators have limited authority, and hence cannot significantly shift the eigenvalues of the system. As a result, the closedloop eigenvalues can be well approximated analytically using perturbati ..."
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Cited by 31 (12 self)
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In this paper we address the problem of lowauthority controller (LAC) design. The premise is that the actuators have limited authority, and hence cannot significantly shift the eigenvalues of the system. As a result, the closedloop eigenvalues can be well approximated analytically using perturbation theory. These analytical approximations may suffice to predict the behavior of the closedloop system in practical cases, and will provide at least a very strong rationale for the first step in the design iteration loop. We will show that LAC design can be cast as convex optimization problems that can be solved efficiently in practice using interiorpoint methods. Also, we will show that by optimizing the ℓ1 norm of the feedback gains, we can arrive at sparse designs, i.e., designs in which only a small number of the control gains are nonzero. Thus, in effect, we can also solve actuator/sensor placement or controller architecture design problems. Keywords: Lowauthority control, actuator/sensor placement, linear operator perturbation theory, convex optimization, secondorder cone programming, semidefinite programming, linear matrix inequality. 1
Nonlinear Optimal Control: A Control Lyapunov Function and Receding Horizon Perspective
 Asian Journal of Control
, 1999
"... Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The online EulerLagrange computation of receding horizon control is naturally viewed in terms of optimal control, whe ..."
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Cited by 27 (0 self)
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Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The online EulerLagrange computation of receding horizon control is naturally viewed in terms of optimal control, whereas researchers in CLF methods have emphasized such notions as inverse optimality. We focus on a CLF variation of Sontag's formula, which also results from a special choice of parameters in the socalled pointwise minnorm formulation. Viewed this way, CLF methods have direct connections with the HamiltonJacobiBellman formulation of optimal control. A single example is used to illustrate the various limitations of each approach. Finally, we contrast the CLF and receding horizon points of view, arguing that their strengths are complementary and suggestive of new ideas and opportunities for control design. The presentation is tutorial, emphasizing concepts and connections over details and t...
Predictive functional control based on fuzzy model for heatexchanger pilot plant
 IEEE Trans. Fuzzy Syst
"... Abstract. In the paper the design methodology and stability analysis of parallel distributed fuzzy model based predictive control is presented. The idea is to design a control law for each rule of the fuzzy model and blend them together. The proposed control algorithm is developed in state space dom ..."
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Cited by 15 (2 self)
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Abstract. In the paper the design methodology and stability analysis of parallel distributed fuzzy model based predictive control is presented. The idea is to design a control law for each rule of the fuzzy model and blend them together. The proposed control algorithm is developed in state space domain and is given in analytical form. The analytical form brings advantages in comparison with optimization based control schemes especially in the sence of realization in realtime. The stability analysis and design problems can be viewed as a linear matrix inequalities problem. This problem is solved by convex programming involving LMIs. In the paper a sufficient stability condition for parallel distributed fuzzy modelbased predictive control is given. The problem is illustrated by an example on magnetic suspension system. Key words: fuzzy identification, predictive control, stability. 1.
Nonlinear Model Predictive Control of Hammerstein and Wiener Models Using Genetic Algorithms
"... Model Predictive Control or MPC can provide robust control for processes with variable gain and dynamics, multivariable interaction, measured loads and unmeasured disturbances. In this paper a novel approach for the implementation of Nonlinear MPC is proposed using Genetic Algorithms (GAs). The prop ..."
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Cited by 10 (1 self)
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Model Predictive Control or MPC can provide robust control for processes with variable gain and dynamics, multivariable interaction, measured loads and unmeasured disturbances. In this paper a novel approach for the implementation of Nonlinear MPC is proposed using Genetic Algorithms (GAs). The proposed method formulates the MPC as an optimization problem and genetic algorithms is used in the optimization process. Application to two types of Nonlinear models namely Hammerstein and Wiener Models is studied and the simulation results are shown for the case of two chemical processes to demonstrate the performance of the proposed scheme.
Model Predictive Control: Multivariable Control Technique of Choice in the 1990s?
 In Advances in Modelbased Predictive Control
, 1990
"... The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived ..."
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Cited by 9 (0 self)
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The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper. 1 Introduction The objective of this paper is to review some major trends in model predictive control (MPC) research with emphasis on recent developments in North America. We will focus on the spirit rather than the details, i.e. we do not attempt to provide a complete list of all the relevant papers published during the last few years. 1 We will try to contrast the motivations driving the research in the different camps. There is...
Feedback Scheduling of Model Predictive Controllers
 Proc. Eighth IEEE RealTime and Embedded Technology and Applications Symp. (RTAS ’02
, 2002
"... The paper presents some preliminary results on dynamic scheduling of model predictive controllers (MPC’s). In model predictive control, the control signal is obtained by optimization of a cost function in each sample, and the MPC task may experience very large variations in execution time. Unique to ..."
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Cited by 7 (0 self)
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The paper presents some preliminary results on dynamic scheduling of model predictive controllers (MPC’s). In model predictive control, the control signal is obtained by optimization of a cost function in each sample, and the MPC task may experience very large variations in execution time. Unique to this application, the cost function also offers an explicit online qualityofservice measure for the task. Based on this insight, a feedback scheduling strategy is proposed, where the scheduler allocates CPU time to the tasks according to the current values of the cost functions. Since the MPC algorithm is iterative, the feedback scheduler may also abort a task prematurely to avoid excessive inputoutput latency. A case study is presented, where the new approach is compared to conventional fixedpriority and earliestdeadlinefirst scheduling. 1.
Control applications of nonlinear convex programming
 the 1997 IFAC Conference on Advanced Process Control
, 1998
"... Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonline ..."
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Cited by 7 (3 self)
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Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interiorpoint algorithms for problem classes such as semide nite programming (SDP) or secondorder cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust openloop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the setpoint and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at
A Predictive Controller with Artificial Lyapunov Function for Linear Systems with Input/State Constraints
, 1998
"... This paper copes with the problem of satisfying input and/or state hard constraints in setpoint tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Procedures to max ..."
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Cited by 7 (0 self)
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This paper copes with the problem of satisfying input and/or state hard constraints in setpoint tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Procedures to maximize the volume of such an ellipsoidal set are provided, and interiorpoint methods to solve online optimization are considered. Key words: Predictive control, Constraints, Lyapunov function, Setpoint control, Optimization problems, Interiorpoint methods, Quadratically constrained quadratic programming. 1 Introduction The necessity of satisfying input/state constraints is a feature that frequently arises in control applications. Constraints are dictated for instance by physical limitations of the actuators or by the necessity to keep some plant variables within safe limits. In recent years, several control techniques have been developed which are able to handle hard constraints, see e....