A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric varia...A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.展开更多
Most of the processes in the industry have nonlinear behavior. Control of such processes with conventional control methods could lead to unstable, suboptimal, etc., results. On the other hand, the adaptive control is ...Most of the processes in the industry have nonlinear behavior. Control of such processes with conventional control methods could lead to unstable, suboptimal, etc., results. On the other hand, the adaptive control is a technique widely used for controlling of nonlinear systems. The approach here is based on the recursive identification of the external linear model as a linear representation of the originally nonlinear system. The controller then reacts to the change of the working point or disturbances which could occur by the change of the parameters, structure, etc. The polynomial synthesis together with the linear quadratic(LQ) approach is employed here for the controller synthesis. These techniques satisfy basic control requirements such as the stability, the reference signal tracking and the disturbance attenuation. Resulted controller could be tuned with the choice of weighting factors in LQ approach. This work investigates the effect of these factors on control results. Proposed methods are tested on the mathematical model of the isothermal continuous stirred-tank reactor and simulated results are also verified on the real model of the continuous stirred tank reactor.展开更多
This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stoc...This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.展开更多
Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, which is actually a control combining the H2 optimization with the H∞ robust performance as the name of ...Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, which is actually a control combining the H2 optimization with the H∞ robust performance as the name of H2/H∞ reveals. Based on the classical theory of linear-quadratic （LQ, for short） optimal control, the sufficient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation （BSRE, for short） associated with H∞ robustness are derived. Then the sufficient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Pdccati equations.展开更多
In safety-critical systems such as transportation aircraft, redundancy of actuators is introduced to improve fault tolerance. How to make the best use of remaining actuators to allow the system to continue achieving a...In safety-critical systems such as transportation aircraft, redundancy of actuators is introduced to improve fault tolerance. How to make the best use of remaining actuators to allow the system to continue achieving a desired operation in the presence of some actuators failures is the main subject of this paper. Considering that many dynamical systems, including flight dynamics of a transportation aircraft, can be expressed as an input affine nonlinear system, a new state repre- sentation is adopted here where the output dynamics are related with virtual inputs associated with the intended operation. This representation, as well as the distribution matrix associated with the effectiveness of the remaining operational actuators, allows us to define different levels of fault tol- erant governability with respect to actuators＇ failures. Then, a two-stage control approach is devel- oped, leading frst to the inversion of the output dynamics to get nominal values for the virtual inputs and then to the solution of a linear quadratic （LQ） problem to compute the solicitation of each operational actuator. The proposed approach is applied to the control of a transportation air- craft which performs a stabilized roll maneuver while a partial failure appears. Two fault scenarios are considered and the resulting performance of the proposed approach is displayed and discussed.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11102031 and 11272076)the Fundamental Research Funds for Central Universities(No.DUT13LK25)+2 种基金the Key Laboratory Fund of Liaoning Province(No.L2013015)the China Postdoctoral Science Foundation(No.2014M550155)the State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.MCMS-0114G02)
文摘A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.
文摘Most of the processes in the industry have nonlinear behavior. Control of such processes with conventional control methods could lead to unstable, suboptimal, etc., results. On the other hand, the adaptive control is a technique widely used for controlling of nonlinear systems. The approach here is based on the recursive identification of the external linear model as a linear representation of the originally nonlinear system. The controller then reacts to the change of the working point or disturbances which could occur by the change of the parameters, structure, etc. The polynomial synthesis together with the linear quadratic(LQ) approach is employed here for the controller synthesis. These techniques satisfy basic control requirements such as the stability, the reference signal tracking and the disturbance attenuation. Resulted controller could be tuned with the choice of weighting factors in LQ approach. This work investigates the effect of these factors on control results. Proposed methods are tested on the mathematical model of the isothermal continuous stirred-tank reactor and simulated results are also verified on the real model of the continuous stirred tank reactor.
基金supported by the National Natural Science Foundation of China(No.71171061)China Postdoctoral Science Foundation(No.2014M552177)+2 种基金the Natural Science Foundation of Guangdong Province(No.S2011010004970)the Doctors Start-up Project of Guangdong University of Technology(No.13ZS0031)the 2014 Guangzhou Philosophy and Social Science Project(No.14Q21).
文摘This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.
文摘Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, which is actually a control combining the H2 optimization with the H∞ robust performance as the name of H2/H∞ reveals. Based on the classical theory of linear-quadratic （LQ, for short） optimal control, the sufficient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation （BSRE, for short） associated with H∞ robustness are derived. Then the sufficient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Pdccati equations.
文摘In safety-critical systems such as transportation aircraft, redundancy of actuators is introduced to improve fault tolerance. How to make the best use of remaining actuators to allow the system to continue achieving a desired operation in the presence of some actuators failures is the main subject of this paper. Considering that many dynamical systems, including flight dynamics of a transportation aircraft, can be expressed as an input affine nonlinear system, a new state repre- sentation is adopted here where the output dynamics are related with virtual inputs associated with the intended operation. This representation, as well as the distribution matrix associated with the effectiveness of the remaining operational actuators, allows us to define different levels of fault tol- erant governability with respect to actuators＇ failures. Then, a two-stage control approach is devel- oped, leading frst to the inversion of the output dynamics to get nominal values for the virtual inputs and then to the solution of a linear quadratic （LQ） problem to compute the solicitation of each operational actuator. The proposed approach is applied to the control of a transportation air- craft which performs a stabilized roll maneuver while a partial failure appears. Two fault scenarios are considered and the resulting performance of the proposed approach is displayed and discussed.
