The optimal feedback control of the linear‐quadratic control problem with a control inequality constraint

Mao, Yunying; Liu, Zeyi

doi:10.1002/oca.685

Cited by 3 publications

(7 citation statements)

References 9 publications

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“…, dx/dt = Ax + bf, x(0) = x o , x(T) = 0, f F , (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) where x is the state vector of dimension 2n. A is the 2n2n plant matrix, B is 2np control matrix, f is the control force vector of dimension p, x(0) is the initial state vector, and x(T) = 0 is the final state of the system.…”

Section: A Minimum Timementioning

confidence: 99%

“…(1-18) Using Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) and (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), the optimal control force f i (t) and trajectory x i (t) can be calculated. However the initial  i (0) for our trajectory with x(0) = x o is not known.…”

Section: A Minimum Timementioning

confidence: 99%

“…For example, if the assume some initial state  i (0) and integrate Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) and (18), we can calculate the function…”

Section: A Minimum Timementioning

confidence: 99%

“…For a solution, the system of Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11) and (1-29) must be integrated along with limits imposed by equation . The norm for the displacements or total deviation can be defined by…”

Section: B Linear Quadratic Regulator (Lqr) With Bounded Controlmentioning

confidence: 99%

“…Problem Statement. The system is described by a linear differential equation in vector form as, It is known the control can have only boundary value in linear system and, if eigenvalues of matrix A is real numbers, the system has only maximum n-1 switches [7]. Problem solution.…”

Section: Solution Of General Linear Optimal Problem For One Controlmentioning

confidence: 99%

See 4 more Smart Citations

Design of Optimal Regulators

Bolonkin

Blvd

Afb³

et al. 2003

2nd AIAA "Unmanned Unlimited" Conf. And Workshop &Amp; Exhibit

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Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of flexible structures, and airplane stability. In all these cases, the focus is in suppressing/decreasing system deviations rapidly. However, if one compares the Linear Quadratic Regulator (LQR) solution with optimal solutions (minimum time), it is seen that the LQR solution is less than optimal in some cases indeed (3-6) times that obtained using a minimum time solution. Moreover, the LQR solution is sometimes unacceptable in practice due to the fact that values of control extend beyond admissible limits and thus the designer must choose coefficients in the linear quadratic form, which are unknown.The authors suggest methods which allow finding a quasi-optimal LQR solution with bounded control which is closed to the minimum time solution. They also remand the process of the minimum time decision.2 3) The "optimal" LQR solution can be up to 3-6 times worse, then the minimum time solution (see the example in this paper). If a researcher chosees to use the LQR solution, the authors suggest a method for limiting maximum control (see point 2) as well as for the choice of selecting the coefficients in the performance index. This allows up to a 2-3 times improvement in the performance index (see accompanying examples) and thus makes the LQR solution acceptable in practical applications.The traditional approach used in the design of a controlled structural system is to design the structure first by satisfying given requirements and then to design the control system. The structure is designed with such constraints placed on weight, allowable stresses, displacements, buckling, general instability, frequency distributions, etc. When the selection of the geometry, cross-sectional area of the members, and material are determined for a specified structure, then the structural frequencies and vibration modes become important input in the design of the control system. Some investigators have written papers discussing an integrated design approach for optimal control. In most references, the control design procedures used, do not take into consideration the limitations on the control forces developed by the actuators, and have not been treated as constraints or design variables. In this paper the problems associated with the selection of the performance index, parameters, weight coefficient in the LQR problem, and limitation of control forces are addressed.In the following sections, theories for the synthesis of an optimal control laws with a quadratic performance index and bounded control forces are given. This is followed by a SISO (Single Input, Single Output) control problem designed using both approaches for comparison of the end state trajectories, with different bounds placed on control forces. Next, the control system for an idealized wing-box is used to illustrate a design application of the m...

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Section: A Minimum Timementioning

confidence: 99%

Section: A Minimum Timementioning

confidence: 99%

Section: A Minimum Timementioning

confidence: 99%

Section: B Linear Quadratic Regulator (Lqr) With Bounded Controlmentioning

confidence: 99%

Section: Solution Of General Linear Optimal Problem For One Controlmentioning

confidence: 99%

See 3 more Smart Citations

Design of Optimal Regulators

Bolonkin

Blvd

Afb³

et al. 2003

2nd AIAA "Unmanned Unlimited" Conf. And Workshop &Amp; Exhibit

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show abstract

The optimal control with infinite horizon of the LQCP with a state constraint

Kang

Mao²

Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826)

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Design of Quadratic Optimal Regulator System for State Space Model of Single phase Inverter both in Standalone and Gridtie Modes

Kiran¹,

Kumar²,

Rao³

2014

Bulletin EEI

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Since in 3-phase systems, the reliability of 3-phase Inverter is not good, under such situations Paralleled Inverter Systems are used. Parallel Inverter operation has a major role in uninterruptible power system (UPS) applications. Most of the standalone inverter systems use a LC filter and proportionalintegral (PI) controller in their control loops. When connecting the paralleled inverters to utility grids, the capacitor becomes redundant and thus either a pure inductor or an LCL filter can be used as inverter output stage. Compared with the L filter, the LCL filter is more attractive because it cannot only provide higher harmonics attenuation with same inductance value, but also allow inverter to operate both in standalone and grid-tie modes, which makes it a universal inverter for distributed generation applications. Output of Inverter should always be checked. In this paper State Space Model of Single phase Inverter is analysis in two modes which are: a) Grid-tie Mode b) Standalone Mode.A Quadratic Optimal Regulator System is designed and its unit step response is obtained to validate whether the whole system (inverter system along with designed QOR) is a stable system or not. This is done using MATLAB Program.

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The optimal feedback control of the linear‐quadratic control problem with a control inequality constraint

Abstract: In this paper, we consider the linear‐quadratic control problem with an inequality constraint on the control variable. We derive the feedback form of the optimal control by the agency of the unconstrained linear‐quadratic control systems. Copyright © 2001 John Wiley & Sons, Ltd.

Cited by 3 publications

References 9 publications

Design of Optimal Regulators

Design of Optimal Regulators

The optimal control with infinite horizon of the LQCP with a state constraint

Design of Quadratic Optimal Regulator System for State Space Model of Single phase Inverter both in Standalone and Gridtie Modes

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