Optimal control of non-well-posed distributed systems
Optimal control of stabilizable time-varying linear systems with time delay
Optimal control of systems determined by strongly nonlinear operator valued measures
In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure...
Optimal control of the Primitive Equations of the ocean with Lagrangian observations
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
Optimal control of unstable non linear evolution systems
Optimal control problem and maximum principle for fractional order cooperative systems
In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...
Optimal control problems on parallelizable riemannian manifolds : theory and applications
The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing calculus...
Optimal control problems on parallelizable Riemannian manifolds: theory and applications
The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group SE(3), which is also a parallelizable Riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions...
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 controllability of impulsive control systems.
Optimal decentralized control design with disturbance decoupling
In this paper we present an input-output point of view for the problem of closed loop norm minimization of stable plants when a decentralized structure and a disturbance decoupling property are imposed on the controller. We show that this problem is convex and present approaches to its solution in the optimal sense in the nontrivial case which is when the block off- diagonal terms of the plant have more columns than rows.
Optimal design of the cooling plunger cavity
An axisymmetric system of mould, glass piece, plunger and plunger cavity is considered. The state problem is given as a stationary head conduction process. The system includes the glass piece representing the heat source and is cooled inside the plunger cavity by flowing water and outside by the environment of the mould. The design variable is taken to be the shape of the inner surface of the plunger cavity. The cost functional is the second power of the norm in the weighted space of difference...
Optimal discrete approximation of continuous linear operators applicable to control problems
Optimal energy decay rate of coupled wave 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 feedback control of a class of distributed-parameter systems with incomplete measurement