Robust near-optimal output feedback control of nonlinear systems

El‐Farra, Nael H.; Christofides, Panagiotis D.

doi:10.1109/acc.2000.876919

Cited by 7 publications

(4 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Methods for robust output feedback controller design and controller-observer synthesizing for various classes of nonlinear systems, have been studied in a number of publications [28]- [30], [31]. An interesting approach for a robust near-optimal feedback controller design is also developed and applied to a chemical reactor in [32].…”

Section: Equation (17a) Is Then Reduced To the Lyapunov Matrix Equatimentioning

confidence: 99%

Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

Ekman

2005

IEEE Trans. Contr. Syst. Technol.

View full text Add to dashboard Cite

A suboptimal solution to the bilinear quadratic regulator problem with infinite final time is studied. The proposed control law is based on the steady-state solution of the state-dependent Riccati equation. A power-series approach of the Riccati equation is presented which results in offline calculations of one Riccati equation and a sequence of Lyapunov equations. Special emphasize is devoted to illustrate the performance of the derived control law applied to the activated sludge process. Index Terms-Activated sludge process (ASP), bilinear systems, power series, Riccati equations, suboptimal control.

show abstract

Section: Equation (17a) Is Then Reduced To the Lyapunov Matrix Equatimentioning

confidence: 99%

Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

Ekman

2005

IEEE Trans. Contr. Syst. Technol.

View full text Add to dashboard Cite

show abstract

“…However, the optimum form of the observer model is considered to be the Kalman filter illustrated years earlier by R. E. Kalman, 3 where they considered the contributions of process and measurement uncertainties and adopted statistical tools to design a gain matrix for minimizing error covariance matrices. 4 Observer models for improvement of process control are very useful for achieving accuracy and processing efficiency, 5,6 especially for complex multivariate process systems like those found in manufacturing plants with multiple products, and biomolecular synthesis with multiple pathways and byproducts. For these kinds of process systems, accurate state measurements may be achieved by employing multiple sensors to measure process output.…”

Section: ■ Introductionmentioning

confidence: 99%

110th Anniversary: Generalized Singular Value Decomposition Reduced-Order Observers for Linear Time-Invariant Systems with Noisy Measurements

Dada

Armaou

2019

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

The use of observers for improvement of output feedback process control is important for achieving accuracy and processing efficiency, especially for large multivariate process systems. Reduced-order observers are particularly advantageous for reducing computational complexity of estimating state variables. The processes considered herein can be modeled as a linear time-invariant continuous system with stochastic elements of modified white Gaussian noise accounting for both process disturbances and sensor inaccuracies. When process measurements are supernumerary to the process states with full rank observation matrix, noise contributions to output measurement are filtered by a soft sensor based on the generalized singular value decomposition (GSVD) solution of best linear unbiased estimation for state variable estimation. When only system observability can be guaranteed, this soft sensor is combined with a reduced-order Kalman-Bucy observer design for continuous estimation of unmeasured state variables at low computation cost. The proposed design procedure is evaluated on a biochemical continuous stirred tank reactor (CSTR) and a simplified Tennessee Eastman model around stable and unstable steady states. The observer is shown to outperform the ordinary Kalman filter design with noisy measurements that deviate from a Gauss-Markov model.

show abstract

“…For continuous‐time single‐input–single‐output nonlinear systems with time‐varying uncertainties, the inverse optimal control approach has also been used for output tracking . In the work of El‐Farra and Christofides, bounded and unbounded robust optimal state‐feedback control laws are proposed to enforce stability and robust asymptotic reference‐input tracking, in the presence of vanishing and nonvanishing uncertain variables.…”

Section: Introductionmentioning

confidence: 99%

“…In the work of El‐Farra and Christofides, bounded and unbounded robust optimal state‐feedback control laws are proposed to enforce stability and robust asymptotic reference‐input tracking, in the presence of vanishing and nonvanishing uncertain variables. Whereas in the other work of El‐Farra and Christofides, where the process states are assumed unmeasured and time‐varying, bounded uncertain variables are considered and robust near‐optimal output‐feedback controllers are synthesized through the combination of a high‐gain observer with a robust optimal state‐feedback controller to achieve exponential stability and asymptotic output tracking. In contrast to the former cases, the proposed unconstrained controller in the work of El‐Farra and Christofides is obtained by reshaping the scalar nonlinear gain of a Lyapunov‐based controller on Sontag's formula, which guarantees the global boundedness of the closed‐loop trajectories and robust asymptotic output tracking with an arbitrary degree of attenuation of the bounded nonvanishing uncertainty effect on the output.…”

Section: Introductionmentioning

confidence: 99%

Inverse optimal control for asymptotic trajectory tracking of discrete‐time stochastic nonlinear systems in block controllable form

Elvira-Ceja

Sánchez

2018

Optim Control Appl Methods

View full text Add to dashboard Cite

This paper concerns an inverse optimal control-based trajectory tracking of discrete-time stochastic nonlinear systems. It is assumed that the nonlinear system can be transformed to the so called nonlinear block controllable form.Additionally, the synthesized control law minimizes a cost functional, which is posteriori determined. In contrast to the optimal control technique, this scheme avoids to solve the stochastic Hamilton-Jacobi-Bellman equation, which is not an easy task. Based on a discrete-time stochastic control Lyapunov function, the proposed optimal controller is analyzed. The proposed approach is applied successfully to the two degrees-of-freedom helicopter with uncertainties in real time. KEYWORDSinverse optimal control, stochastic nonlinear systems, trajectory tracking INTRODUCTIONOptimal stochastic control is related to determining a control law for a given stochastic system, such that the a priori cost functional is minimized; the major drawback is solving the associated stochastic Hamilton-Jacobi-Bellman equation, 1 which is difficult or even impossible to solve. However, in the work of Zhang et al, 2 the optimal control of discrete-time nonlinear stochastic systems is solved based on discrete martingale theory. To overcome the solution of the stochastic Hamilton-Jacobi-Bellman equation, Crandall and Lions 3 introduced a weak solution named as viscosity solution, whereas Krstić et al 4 used the inverse optimal control approach in continuous-time nonlinear systems with uncertainties for stabilization, regulation, and tracking 3,4 ; consider the continuous-time case. On the other hand, the neural network-based approximation methods have been used to solve the optimal control problem via adaptive dynamic programming, such as in the works of Luy, 5,6 where the cooperative control, for stabilization and tracking respectively, of multiple multiple-input-multiple-output nonlinear systems in strict feedback with no knowledge of internal system dynamics and affected by external disturbances is addressed.This paper proposes an inverse optimal control law for asymptotic stability in probability, along a desired trajectory, of discrete-time stochastic nonlinear systems in nonlinear block controllable (NBC) form. Using this approach, a feedback control law, based on the a priori knowledge of a discrete-time stochastic control Lyapunov function (DSCLF), is synthesized first, and then it is established that this control law optimizes a cost functional.The inverse optimal control approach of deterministic systems is presented for the continuous 7-11 and discrete-time 12-14 case, respectively. Although the inverse optimal control for continuous-time stochastic nonlinear systems has been

show abstract

Robust near-optimal output feedback control of nonlinear systems

Cited by 7 publications

References 34 publications

Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

110th Anniversary: Generalized Singular Value Decomposition Reduced-Order Observers for Linear Time-Invariant Systems with Noisy Measurements

Inverse optimal control for asymptotic trajectory tracking of discrete‐time stochastic nonlinear systems in block controllable form

Contact Info

Product

Resources

About