scholarly journals On guarantee optimization in control problem with finite set of disturbances

2021 ◽  
Vol 31 (4) ◽  
pp. 613-628
Author(s):  
M.I. Gomoyunov ◽  
D.A. Serkov
Keyword(s):  
Control Problem ◽  
Control Strategies ◽  
Continuous Functions ◽  
Functional Constraint ◽  
Memory Strategies ◽  
Memory Strategy ◽  
Classical Formulation ◽  
Technical Assumption ◽  
Finite Set ◽  
Piecewise Continuous

In this paper, we deal with a control problem under conditions of disturbances, which is stated as a problem of optimization of the guaranteed result. Compared to the classical formulation of such problems, we assume that the set of admissible disturbances is finite and consists of piecewise continuous functions. In connection with this additional functional constraint on the disturbance, we introduce an appropriate class of non-anticipative control strategies and consider the corresponding value of the optimal guaranteed result. Under a technical assumption concerning a property of distinguishability of the admissible disturbances, we prove that this result can be achieved by using control strategies with full memory. As a consequence, we establish unimprovability of the class of full-memory strategies. A key element of the proof is a procedure of recovering the disturbance acting in the system, which allows us to associate every non-anticipative strategy with a full-memory strategy providing a close guaranteed result. The paper concludes with an illustrative example.

scholarly journals Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yessica Hernández-Eliseo ◽  
Josué Ramírez-Ortega ◽  
Francisco G. Hernández-Zamora
Keyword(s):  
Toeplitz Operators ◽  
Continuous Functions ◽  
Two Dimensional ◽  
Siegel Domain ◽  
Limit Values ◽  
Type Space ◽  
Measurable Functions ◽  
Finite Set ◽  
Type Spaces ◽  
Piecewise Continuous

We describe certain C ∗ -algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D 2 ⊂ ℂ 2 . Bounded measurable functions of the form c Im   ζ 1 , Im   ζ 2 − ζ 1 2 are called nilpotent symbols. In this work, we consider symbols of the form a Im   ζ 1 b Im   ζ 2 − ζ 1 2 , where both limits lim s → 0 + b s and lim s → + ∞ b s exist, and a s belongs to the set of piecewise continuous functions on ℝ ¯ = − ∞ , + ∞ and having one-side limit values at each point of a finite set S ⊂ ℝ . We prove that the C ∗ -algebra generated by all Toeplitz operators T a b is isomorphic to C Π ¯ , where Π ¯ = ℝ ¯ × ℝ ¯ + and ℝ ¯ + = 0 , + ∞ .

Finite-Set Model-Predictive Control Strategies for a 3L-NPC Inverter Operating With Fixed Switching Frequency

2018 ◽  
Vol 65 (5) ◽  
pp. 3954-3965 ◽  
Author(s):  
Felipe Donoso ◽  
Andres Mora ◽  
Roberto Cardenas ◽  
Alejandro Angulo ◽  
Doris Saez ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Control Strategies ◽  
Switching Frequency ◽  
Finite Set

scholarly journals On geometric duality for state-constrained control problems

1979 ◽  
Vol 20 (2) ◽  
pp. 301-312
Author(s):  
T.R. Jefferson ◽  
C.H. Scott
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
State Constraints ◽  
Strong Duality ◽  
State Constraint ◽  
Continuous Functions ◽  
Control Problems ◽  
Absolutely Continuous Functions ◽  
Pure State Constraints ◽  
Constrained Control Problems

For convex optimal control problems without explicit pure state constraints, the structure of dual problems is now well known. However, when these constraints are present and active, the theory of duality is not highly developed. The major difficulty is that the dual variables are not absolutely continuous functions as a result of singularities when the state trajectory hits a state constraint. In this paper we recognize this difficulty by formulating the dual probram in the space of measurable functions. A strong duality theorem is derived. This pairs a primal, state constrained convex optimal control problem with a dual convex control problem that is unconstrained with respect to state constraints. In this sense, the dual problem is computationally more attractive than the primal.

scholarly journals Distributed Consensus-Based Robust Adaptive Formation Control for Nonholonomic Mobile Robots with Partial Known Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zhaoxia Peng ◽  
Shichun Yang ◽  
Guoguang Wen ◽  
Ahmed Rahmani
Keyword(s):  
Control Problem ◽  
Mobile Robots ◽  
Formation Control ◽  
Control Strategies ◽  
Reference Trajectory ◽  
Consensus Problem ◽  
Distributed Consensus ◽  
Nonholonomic Mobile Robots ◽  
Robust Adaptive ◽  
Virtual Leader

This paper investigates the distributed consensus-based robust adaptive formation control for nonholonomic mobile robots with partially known dynamics. Firstly, multirobot formation control problem has been converted into a state consensus problem. Secondly, the practical control strategies, which incorporate the distributed kinematic controllers and the robust adaptive torque controllers, are designed for solving the formation control problem. Thirdly, the specified reference trajectory for the geometric centroid of the formation is assumed as the trajectory of a virtual leader, whose information is available to only a subset of the followers. Finally, numerical results are provided to illustrate the effectiveness of the proposed control approaches.

Note on an Application of the δ-Function in the Representation of Solutions of Algebraic Equations

1967 ◽  
Vol 10 (5) ◽  
pp. 735-738
Author(s):  
J. B. Sabat
Keyword(s):  
Continuous Function ◽  
Delta Function ◽  
Continuous Functions ◽  
Dirac Delta Function ◽  
Algebraic Equations ◽  
Dirac Delta ◽  
Representation Of Solutions ◽  
Piecewise Continuous ◽  
Image Position

The “function” δ(x - xo) is known as the Dirac Delta function and may be defined as zero everywhere except at xo, where it is infinite in such a way that1having property that for every continuous function φ(x) on (a, b)2It is well known [2] δ(x-xo) can be approximated as a limit of a sequence of piecewise continuous functions, and there is an abundance of such sequences.

Some explicit results on one kind of sticky diffusion

2019 ◽  
Vol 56 (2) ◽  
pp. 398-415
Author(s):  
Yiming Jiang ◽  
Shiyu Song ◽  
Yongjin Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Functions ◽  
Price Dynamics ◽  
Call Option ◽  
Distributional Properties ◽  
Financial Application ◽  
Piecewise Continuous

AbstractIn this paper we derive several explicit results on one special sticky diffusion process which is constructed as a time-changed version of a diffusion with no sticky points. A theorem concerning the process-related Green operators defined on some nonnegative piecewise continuous functions is provided. Then, based on this theorem, we explore the distributional properties of the sticky diffusion. A financial application is presented where we compute the value of the European vanilla call option written on the underlying with sticky price dynamics.

scholarly journals FPGA-Based Implementation of Finite Set-MPC for a VSI System Using XSG-Based Modeling

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 260 ◽  
Author(s):  
Vijay Kumar Singh ◽  
Ravi Nath Tripathi ◽  
Tsuyoshi Hanamoto
Keyword(s):  
Real Time ◽  
System Development ◽  
Control Strategies ◽  
System Modeling ◽  
Experimental System ◽  
Experimental Result ◽  
Voltage Source ◽  
Primary Concern ◽  
Fpga Design ◽  
Finite Set

Finite set-model predictive control (FS-MPC) is used for power converters and drives having unique advantages as compared to the conventional control strategies. However, the computational burden of the FS-MPC is a primary concern for real-time implementation. Field programmable gate array (FPGA) is an alternative and exciting solution for real-time implementation because of the parallel processing capability, as well as, discrete nature of the hardware platform. Nevertheless, FPGA is capable of handling the computational requirements for the FS-MPC implementation, however, the system development involves multiple steps that lead to the time-consuming debugging process. Moreover, specific hardware coding skill makes it more complex corresponding to an increase in system complexity that leads to a tedious task for system development. This paper presents an FPGA-based experimental implementation of FS-MPC using the system modeling approach. Furthermore, a comparative analysis of FS-MPC in stationary αβ and rotating dq frame is considered for simulation as well as experimental result. The FS-MPC for a three-phase voltage source inverter (VSI) system is developed in a realistic digital simulator integrated with MATLAB-Simulink. The simulated controller model is further used for experimental system implementation and validation using Xilinx FPGA: Zedboard Zynq Evaluation and Development Kit. The digital simulator termed as Xilinx system generator (XSG) provided by Xilinx is used for modeling-based FPGA design.

scholarly journals Synthesis of intelligent fuzzy control in the space of bounded piecewise-continuous functions based on the combined maximum principle

2018 ◽  
Vol 226 ◽  
pp. 04031 ◽  
Author(s):  
Andrey A. Kostoglotov ◽  
Sergey V. Lazarnko ◽  
Igor A. Nikitin
Keyword(s):  
Control Method ◽  
Control Object ◽  
Continuous Functions ◽  
Terminal State ◽  
Control Synthesis ◽  
Continuous Control ◽  
Control Laws ◽  
Relay Control ◽  
Piecewise Continuous ◽  
Two Stages

It is shown that the solution of the problem of control synthesis using the Hamilton-Ostrogradskii principle leads to a variational inequality, from which the conditions for the maximum of the the generalized power function in the space of bounded piecewise continuous functions follow. It allows to find a feedback structure up to a synthesis function. Using the methods of the structure construction the nonlinear structures of the relay and continuous control laws are obtained. The proposed control method allows to avoid the mode with frequented switching. It consists of the following two stages. At the first stage, the control object is brought into the vicinity of the terminal state using the relay control law. In the second stage, the quasi-optimal continuous control is used. The uncertainty of the transition area size is resolved using fuzzy logic. The efficiency of the intelligent controls is demonstrated by the example of mathematical modeling of the system dynamics.

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