scholarly journals Analytical design of controllers for discrete-continuous systems with linear control

2021 ◽  
Vol 12 (2) ◽  
pp. 121-135
Author(s):  
Irina Viktorovna Rasina ◽  
Oles Vladimirovich Fesko ◽  
Oleg Valerievich Usenko
Keyword(s):  
Optimality Conditions ◽  
Linear Control ◽  
Sufficient Optimality Conditions ◽  
Continuous Systems ◽  
Analytical Design ◽  
State Dependent ◽  
Optimal Controllers

The study focuses on a certain kind of discrete-continuous systems (DCS): the linear hybrid DCS with state-dependent coefficients. The authors proposed a problem similar to the analytical design of optimal controllers (ADOC). For this study, we generalized the Krotov sufficient optimality conditions. The paper includes several examples.

scholarly journals Analytical design of controllers for discrete-continuous systems with linear control

2021 ◽  
Vol 12 (2) ◽  
pp. 105-119
Author(s):  
Ирина Викторовна Расина ◽  
Олесь Владимирович Фесько ◽  
Олег Валерьевич Усенко
Keyword(s):  
Linear Control ◽  
Continuous Systems ◽  
Analytical Design

Рассматривается одна из разновидностей дискретно/непрерывных систем — линейные по управлению ДНС с коэффициентами, зависящими от состояния, относящиеся к гибридным системам. Формулируется аналог задачи аналитического конструирования регуляторов (АКОР). Для исследования используется обобщение достаточных условий оптимальности Кротова. Приводятся иллюстративные примеры.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

scholarly journals Sufficient optimality conditions for extremal controls based on functional increment formulas

2017 ◽  
Vol 7 (2) ◽  
pp. 191-199
Author(s):  
Vladimir Srochko ◽  
◽  
Vladimir Antonik ◽  
Elena Aksenyushkina ◽  
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions

scholarly journals A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs ◽  
Necessary And Sufficient

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

scholarly journals Numerical Solution of SDRE Control Problem – Comparison of the Selected Methods

2020 ◽  
Vol 45 (2) ◽  
pp. 79-95
Author(s):  
Krzysztof Hałas ◽  
Eugeniusz Krysiak ◽  
Tomasz Hałas ◽  
Sławomir Stępień
Keyword(s):  
Control Systems ◽  
Riccati Equation ◽  
Computational Effort ◽  
Linear Control ◽  
Algebraic Riccati Equation ◽  
Linear Control Systems ◽  
Nonlinear Constraints ◽  
State Dependent ◽  
Suboptimal Solution ◽  
Problem Comparison

AbstractMethods for solving non-linear control systems are still being developed. For many industrial devices and systems, quick and accurate regulators are investigated and required. The most effective and promising for nonlinear systems control is a State-Dependent Riccati Equation method (SDRE). In SDRE, the problem consists of finding the suboptimal solution for a given objective function considering nonlinear constraints. For this purpose, SDRE methods need improvement.In this paper, various numerical methods for solving the SDRE problem, i.e. algebraic Riccati equation, are discussed and tested. The time of computation and computational effort is presented and compared considering selected nonlinear control plants.

scholarly journals Optimal Factorization of the State-Dependent Riccati Equation Technique in a Satellite Attitude and Orbit Control System

2021 ◽  
Vol 20 ◽  
pp. 98-107
Author(s):  
Alessandro Gerlinger Romero ◽  
Luiz Carlos Gadelha De Souza
Keyword(s):  
Control System ◽  
Riccati Equation ◽  
The State ◽  
Linear Control ◽  
Control Techniques ◽  
Orbit Control ◽  
Satellite Attitude ◽  
Modified Rodrigues Parameters ◽  
State Dependent ◽  
Attitude Maneuver

The satellite attitude and orbit control system (AOCS) can be designed with success by linear control theory if the satellite has slow angular motions and small attitude maneuver. However, for large and fast maneuvers, the linearized models are not able to represent all the perturbations due to the effects of the nonlinear terms present in the dynamics and in the actuators (e.g., saturation). Therefore, in such cases, it is expected that nonlinear control techniques yield better performance than the linear control techniques. One candidate technique for the design of AOCS control law under a large maneuver is the State-Dependent Riccati Equation (SDRE). SDRE entails factorization (that is, parameterization) of the nonlinear dynamics into the state vector and the product of a matrix-valued function that depends on the state itself. In doing so, SDRE brings the nonlinear system to a (nonunique) linear structure having state-dependent coefficient (SDC) matrices and then it minimizes a nonlinear performance index having a quadratic-like structure. The nonuniqueness of the SDC matrices creates extra degrees of freedom, which can be used to enhance controller performance, however, it poses challenges since not all SDC matrices fulfill the SDRE requirements. Moreover, regarding the satellite's kinematics, there is a plethora of options, e.g., Euler angles, Gibbs vector, modified Rodrigues parameters (MRPs), quaternions, etc. Once again, some kinematics formulation of the AOCS do not fulfill the SDRE requirements. In this paper, we evaluate the factorization options (SDC matrices) for the AOCS exploring the requirements of the SDRE technique. Considering a Brazilian National Institute for Space Research (INPE) typical mission, in which the AOCS must stabilize a satellite in three-axis, the application of the SDRE technique equipped with the optimal SDC matrices can yield gains in the missions. The initial results show that MRPs for kinematics provides an optimal SDC matrix.

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