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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  , a random logistic model with time-independent coefficients is studied using the so-called sample approach  . ...doi:10.1016/j.aml.2011.06.024 fatcat:p7gmylrw65g6di6cwb2fdnbrhy
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
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
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
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. ...
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 ...
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. ...
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
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
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
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
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
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
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
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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