Receding horizon control of nonlinear systems

Mayne, D. Q.; Michalska, H.

doi:10.1109/9.57020

Cited by 836 publications

(287 citation statements)

References 7 publications

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“…Predictive control strategies were extensively and successfully tested in realworld process control applications, sparking even greater interest from researchers. Despite the growing popularity of the technique, solid theoretical analyses and stability proofs appeared only in the 90s, with the seminal works of Mayne et al [9][10][11], Bemporad and Morari [12], Rawlings and Muske [13], and Bitmead and Gevers [14], among others. Theoretical works also started to appear that were applicable to nonlinear systems.…”

Section: B Overview Of Model-predictive Controlmentioning

confidence: 99%

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Multiplexed Predictive Control of a Large Commercial Turbofan Engine

Richter

Singaraju

Litt

2008

Journal of Guidance, Control, and Dynamics

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Model predictive control is a strategy well-suited to handle the highly complex, nonlinear, uncertain, and constrained dynamics involved in aircraft engine control problems. However, it has thus far been infeasible to implement model predictive control in engine control applications, because of the combination of model complexity and the time allotted for the control update calculation. In this paper, a multiplexed implementation is proposed that dramatically reduces the computational burden of the quadratic programming optimization that must be solved online as part of the model-predictive-control algorithm. Actuator updates are calculated sequentially and cyclically in a multiplexed implementation, as opposed to the simultaneous optimization taking place in conventional model predictive control. Theoretical aspects are discussed based on a nominal model, and actual computational savings are demonstrated using a realistic commercial engine model.

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Section: B Overview Of Model-predictive Controlmentioning

confidence: 99%

“…Although nonlinear versions of MPC exist that guarantee stability and can work with constraints [10,11], they are not applicable to our engine control problem without a number of simplifications and assumptions. The approach taken is reasonable in view of problem constraints.…”

Section: Mpc For Aircraft Propulsionmentioning

confidence: 99%

Multiplexed Predictive Control of a Large Commercial Turbofan Engine

Richter

Singaraju

Litt

2008

Journal of Guidance, Control, and Dynamics

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“…An intermediate approach that could be used here between the open-and closed-loop approach is the receding-horizon control of linear infinite-dimensional systems (see for example [25][26][27]). This approach approximates the optimal infinite-horizon control with a finite-horizon suboptimal control, where the horizon goes from the current time to the current time plus a fixed horizon length and, in the most naive implementation, the state variable is constrained at the final time.…”

Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 99%

Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

et al. 2006

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Time-dependent acoustic scattering problems involving "smart" obstacles are considered. When hit by an incident acoustic field, smart obstacles react in an attempt to pursue a preassigned goal. Let IR 3 be the three-dimensional real Euclidean space, and let ⊂ IR 3 be a bounded simply connected open set with a Lipschitz boundary characterized by a constant acoustic boundary impedance χ , immersed in an isotropic and homogeneous medium that fills IR 3 \ . The closure of will be denoted as . When hit by an incident field, the obstacle pursues the preassigned goal through the action of a control input acting on its boundary (i.e., a quantity with dimensions of a pressure divided by a time). The obstacles considered in this paper monitor the control input acting on their boundaries in order to achieve one of the following goals: (i) be furtive in a given set of the frequency space, and (ii) appear in a given set of the frequency space and outside a given set of IR 3 containing and G as similar as possible to a "ghost" obstacle G having boundary acoustic impedance χ G . It is assumed that ∩ G = ∅ and G = ∅. The problem corresponding to the first goal will be called the definite-band furtivity problem, and the problem corresponding to the second goal will be called the definite-band ghost-obstacle problem. These two L. Fatone 386 J Eng Math (2006) 56:385-413 goals define two classes of smart obstacles. In this paper, these problems are modeled as optimal-control problems for the wave equation introducing a control input acting on the boundary of for time t ∈ IR. The cost functionals proposed depend on the value of the control input on the boundary of the obstacle and on the value of the scattered acoustic field generated by the obstacle on the boundary in the "furtivity case", and on the boundary of a suitable set containing and G in the "ghost-obstacle case". Under some assumptions, the use of the Pontryagin maximum principle allows us to formulate the first-order optimality conditions for the definite-band furtivity problem and for the definite-band ghost-obstacle problem as exterior problems outside the obstacle for a system of two coupled wave equations. Numerical methods to solve these exterior problems are developed by extending previous work. These methods belong to the class of the operator-expansion methods that are highly parallelizable. Numerical experiments proving the validity of the control problems proposed as mathematical models of the definite-band furtivity problem and definite-band ghost obstacle problem are presented. The numerical results obtained with a parallel implementation of the numerical methods developed are discussed and their properties are established. The speed-up factors obtained using parallel computing are really impressive. The website: http://www.econ.univpm.it/recchioni/w11 contains animations and virtual reality applications relative to the numerical experiments.

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“…The studies [2][3][4][5][6][7][8] analyze the first part of this problem (changing over a system from one state to another) and its second part (stabilization of the system in the new equilibrium position). The purpose of the present paper is to describe a method of solving the problem in a class of bounded controls for a nonlinear system and providing additional properties of transient processes.…”

Section: Introductionmentioning

confidence: 99%

Realization of a bounded feedback in a nonlinear control problem

2009

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We substantiate a method for design of a limited feedback to control a system whose mathematical model includes a nonlinear state function. Designing such a feedback is based on a positional solution of auxiliary optimal control problems which provides the transition from the vicinity of one equilibrium state to the vicinity of a new equilibrium state and stabilization of the system in the new state. Preassigned additional constrains on the trajectory of the control system are satisfied.

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Receding horizon control of nonlinear systems

Cited by 836 publications

References 7 publications

Multiplexed Predictive Control of a Large Commercial Turbofan Engine

Multiplexed Predictive Control of a Large Commercial Turbofan Engine

Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

Realization of a bounded feedback in a nonlinear control problem

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