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Solving Riccati time-dependent models with random quadratic coefficients

J.-C. Cortés, L. Jódar, R. Company, L. Villafuerte
2011 Applied Mathematics Letters  
This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition  ...  Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity.  ...  These types of models have been considered in different scenarios. In [1] , a random logistic model with time-independent coefficients is studied using the so-called sample approach [2] .  ... 
doi:10.1016/j.aml.2011.06.024 fatcat:p7gmylrw65g6di6cwb2fdnbrhy

A low-rank solution method for Riccati equations with indefinite quadratic terms [article]

Peter Benner, Jan Heiland, Steffen W. R. Werner
2021 arXiv   pre-print
In this paper, we develop an iterative method to compute low-rank approximations of stabilizing solutions of large-scale sparse continuous-time algebraic Riccati equations with indefinite quadratic terms  ...  Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design.  ...  Conclusions We have developed a low-rank iterative method for solving large-scale sparse Riccati equations with indefinite quadratic terms, which is based on solutions of Riccati equations with negative  ... 
arXiv:2111.06516v1 fatcat:l7kyxamttnavvmilrsxpyzkjdm

Linear-quadratic optimal control under non-Markovian switching

Fulvia Confortola, Marco Fuhrman, Giuseppina Guatteri, Gianmario Tessitore
2018 Stochastic Analysis and Applications  
Keywords: Linear-quadratic optimal control, optimal control with stochastic coefficients, Riccati backward stochastic differential equations (Riccati BSDE).  ...  We admit stochastic coefficients, possibly depending on an underlying independent marked point process, so that our model is general enough to include controlled switching systems where the switching mechanism  ...  The use of a random cost functional is customary when dealing with stochastic coefficients, but since E F0 = E this models generalizes the previous ones when t = 0.  ... 
doi:10.1080/07362994.2017.1381624 fatcat:eca6vdy4tbfbpcgbz2xauxg7yq

LINEAR QUADRATIC CONTROL PROBLEM OF STOCHASTIC SWITCHING SYSTEMS WITH DELAY

Charkaz Arif Aghayeva
2016 Anadolu University journal of science and techonology - b - theoretical sciences  
The contribution of this paper is to investigate the stochastic optimal control problem of linear switching systems with quadratic cost functional.  ...  Linear Quadratic (LQ) problems constitute important class of optimal control problems.  ...  The differential equations with time delay can be used to model the processes with a memory [3, 4] .  ... 
doi:10.20290/btdb.87745 fatcat:4thq5jragzdcleuxcqwufepilq

Page 388 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
T.(1-UCLA-C) 85a:93172 On discrete-time Riccati-like matrix difference equations with random coefficients. Internat. J. Systems Sct. 14 (1983), no. 4, 385-407.  ...  The general problem (with drift) is then solved by an application of this result and the Girsanov transformation.” Panossian, Hagop; Leondes, C.  ... 

Page 720 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
We assume dependent arrival and service processes as is usually the case in models of bursty traffic.  ...  Summary: “In this paper, we consider the class of infinite- dimensional discrete-time linear systems with multiplicative random disturbances (i.e. with the state multiplied by a ran- dom sequence), also  ... 

Page 5888 of Mathematical Reviews Vol. , Issue 89J [page]

1989 Mathematical Reviews  
The kinematic model is perturbed by Gaussian white noises that model a time-dependent random environment.  ...  ity with a rectangular box shape around given nominal values of the polynomial coefficients.  ... 

The Quadratic-Quadratic Regulator Problem: Approximating feedback controls for quadratic-in-state nonlinear systems [article]

Jeff Borggaard, Lizette Zietsman
2019 arXiv   pre-print
This approach is amenable to feedback laws with low degree polynomials but have a relatively modest model dimension that could be achieved by modern model reduction methods.  ...  This is significantly more challenging and holds the LQR as special case that must be solved along the way.  ...  This paper addresses this by specifically solving the quadratic-quadratic regulator problem: minimizing a quadratic cost subject to a state equation with a quadratic nonlinearity.  ... 
arXiv:1910.03396v1 fatcat:ektsfq4xkve6xcpt2rzxa2q7qq

Solution of matrix Riccati differential equation for nonlinear singular system using neural networks

J. Abdul Samath, N. Selvaraju
2010 International Journal of Computer Applications  
In this paper, the solution of the matrix Riccati differential equation(MRDE) for nonlinear singular system is obtained using neural networks.  ...  The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the MRDE obtained from well known traditional Runge Kutta(RK)method and nontraditional neural network method  ...  This nonlinear quadratic (NLQ) method applies to systems having a broad class of nonlinear dynamics with state dependent weighting matrices.  ... 
doi:10.5120/575-181 fatcat:yv4tahm23vgfpgkzu25evaijyi

State Dependent Riccati Equation Control of an Active Hydro-Pneumatic Suspension System

Ferhat Sağlam, Y. Samim Ünlüsoy
2014 Journal of Automation and Control Research  
A linear structured model with state dependent matrices of the nonlinear quarter car model is derived for use in controller design.  ...  A nonlinear control method, State Dependent Riccati Equation control (SDRE) is used to attenuate sprung mass acceleration, suspension deflection, and tire deflection.  ...  By using this model and states, SDRE is solved at each time step with changing states.  ... 
doi:10.11159/jacr.2014.001 fatcat:bol4gin73jh2ro4ebexx7g67tq

Linear-quadratic optimal control under non-Markovian switching [article]

Fulvia Confortola, Marco Fuhrman, Giuseppina Guatteri, Gianmario Tessitore
2016 arXiv   pre-print
The problem is solved by means of a Riccati equation, which a backward stochastic differential equation driven by the Bronwian motion and by the random measure associated to the marked point process.  ...  We admit stochastic coefficients, possibly depending on an underlying independent marked point process, so that our model is general enough to include controlled switching systems where the switching mechanism  ...  The use of a random cost functional is customary when dealing with stochastic coefficients, but since E F0 = E this models generalizes the previous ones when t = 0.  ... 
arXiv:1609.04977v1 fatcat:p5gjbtenivcvfnjzexldp65d2y

Optimal control for stochastic nonlinear singular system using neural networks

N. Kumaresan, P. Balasubramaniam
2008 Computers and Mathematics with Applications  
In this paper, optimal control for stochastic nonlinear singular system with quadratic performance is obtained using neural networks.  ...  The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the matrix Riccati differential equation (MRDE) obtained from the well-known traditional Runge-Kutta (RK  ...  This nonlinear quadratic (NLQ) method applies to systems having a broad class of nonlinear dynamics with state-dependent weighting matrices.  ... 
doi:10.1016/j.camwa.2008.03.041 fatcat:mnboiqnqg5cfllabiwwdgghhfm

Optimal Solution to Matrix Riccati Equation – For Kalman Filter Implementation [chapter]

Bhar K., Charles A., Lanre M.A., Aliyu A.
2012 MATLAB - A Fundamental Tool for Scientific Computing and Engineering Applications - Volume 3  
This command solves a continuous time Algebraic Riccati Equation associated with the described model.  ...  More generally, "Riccati equations" refer to matrix equations with analogous quadratic terms both in continuous-time and in discrete-time Linear-Quadratic-Gaussian Control.  ... 
doi:10.5772/46456 fatcat:b65vkdtzuzfw5knvkhaem2bsuu

A Time-Periodic Control Law for Satellite Magnetic Stabilization

Adrian-Mihail Stoica, Vasile Dragan
2017 International Journal of Modeling and Optimization  
The design method is based on using an optimal 2 H controller with periodic coefficients. These coefficients depend on the solution of a specific system of coupled Riccati type equations.  ...  Index Terms-2 H optimal control, satellite stabilization, system of coupled Riccati equations, time periodic control law.  ...  It was shown that the optimal 2 H controller is time varying with time-periodic coefficients.  ... 
doi:10.7763/ijmo.2017.v7.578 fatcat:tj7qafboyzecbkkxi46hxdyyi4

Two Inverse Problems Solution by Feedback Tracking Control

Vladimir Turetsky
2021 Axioms  
The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation.  ...  Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed.  ...  In this paper, we deal with the input and time-varying coefficients restoration problems for a system, modeled by a linear differential equation, based on noisy output measurements.  ... 
doi:10.3390/axioms10030137 fatcat:ejnlvecribf3do5veilypxblbe
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