Optimal control for third degree polynomial systems.
Optimal control of a linear discrete system
Optimal control of a production system with inventory-level-dependent demand.
Optimal control of a stochastic heat equation with boundary-noise and boundary-control
We are concerned with the optimal control of a nonlinear stochastic heat equation on a bounded real interval with Neumann boundary conditions. The specificity here is that both the control and the noise act on the boundary. We start by reformulating the state equation as an infinite dimensional stochastic evolution equation. The first main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The C1 regularity...
Optimal control of deteriorating production inventory systems.
Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
Optimal control of impulsive stochastic evolution inclusions
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability
In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see [chen], for finite dimensional stochastic equations or [UC], for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see [1990], [ukl])....
Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics
This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...
Optimal control solution for Pennes' equation using strongly continuous semigroup
A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction...
Optimal control under discrete observation of continuous stochastic systems with time delay
Optimal control with partial information for stochastic Volterra equations.
Optimal erasures in decision-feedback equalization for the Gaussian noise
A new method of optimizing decision feedback parameters for intersymbol interference equalizers is described. The coefficient existing in the decision feedback loop depends on risk qualification of the received decision. We prove that bit error probability can be decreased with this method for any channel with a single interference sample and small Gaussian noise. Experimental results are presented for selected channels. The dependences of optimal feedback parameters on channel interference samples...
Optimal estimator of hypothesis probability for data mining problems with small samples
The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "Epₕ√2 completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute...
Optimal filtering for bilinear system states and its application to terpolymerization process identification.
Optimal guaranteed cost filtering for Markovian jump discrete-time systems.
Optimal investment strategy for a non-life insurance company: quadratic loss
The aim of this paper is to construct an optimal investment strategy for a non-life insurance business. We consider an insurance company which provides, in exchange for a single premium, full coverage to a portfolio of risks which generates losses according to a compound Poisson process. The insurer invests the premium and trades continuously on the financial market which consists of one risk-free asset and n risky assets (Black-Scholes market). We deal with the insurer's wealth path dependent disutility...
Optimal investment under stochastic volatility and power type utility function
2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.
Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals.
Optimal multivariable PID regulator
A continuous version of optimal LQG design under presence of Wiener disturbances is solved for MIMO controlled plant. Traditional design tools fail to solve this problem due to unstability of the augmented plant. A class of all optimality criteria, which guarantee existence of an asymptotical solution, is defined using a plant deviation model. This class is utilized in design of an optimal state and an error feedback regulator which is presented here. The resultant optimal error regulator is interpreted...