An infinite-horizon optimal control problem with a free right endpoint is considered. In this paper we proved that Lyapunov stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution.

In this paper fuel-optimal rendezvous maneuvers for passenger cars will be analyzed. The results are obtained using simplified yet realistic descriptions of the vehicles and their internal combustion engines. Both the mathematical arguments leading to and the physical interpretations deriving from the optimal solution are shown. Implementation issues (computational burden, convergence, feedforw...

Let G be a bounded domain in R" and Q = G X (0, T). We consider the solution^«) of the pseudo-parabolic initial-value problem (1 + M(x))y,(u) + L(x)y(u) = u in L2(Q), y(-,0;u) = 0 in L2(G), to be the state corresponding to the control u. Here M(x) and L{x) are symmetric uniformly strongly elliptic second-order partial differential operators. The control problem is to find a control un in a fixe...

We discuss a framework for coordinating the response of distributed energy resources (DERs) connected to electric power distribution networks to provide frequency regulation services. These resources include plug-in electric vehicles, thermostatically controlled loads, and microturbines. In this framework, we consider an aggregator that participates in the real-time market by submitting an offe...

The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within its frame, the third evolution equation is developed. This equation only solves the control variables along the variation time to get the optimal solution, and...

In this paper, we attempt to solve the time-optimal control problem for single-degree-of-freedom (DOF) mechanical systems with friction, while taking into account not only the velocity-dependent control input constraint but also the state constraint. Direct application of the Pontryagin’s maximum principle (PMP) leads to a sixth-order nonlinear two-point boundary-value problem (TPBVP) which is ...

Measure valued optimal control control problems governed by the linear wave equation are analyzed. The space of vector measures M(Ωc, L2(I)) is chosen as control space and the corresponding total variation norm as control cost functional. The support of the controls (sparsity pattern) is time-independent which is desired in many applications, e.g., inverse problems or optimal actuator placement...

Ameliorating products are frequently seen in stock management. Considering ramp type pattern of time dependent demand for such products is a justification for the development of related inventory theory. In a recently published paper by Singh et al. (2011), such kind of problem is discussed. However, the solution given by author is incomplete because that fails to depict the case for optimal re...

Our motor system changes due to causes that span multiple timescales. For example, muscle response can change because of fatigue, a condition where the disturbance has a fast timescale or because of disease where the disturbance is much slower. Here we hypothesize that the nervous system adapts in a way that reflects the temporal properties of such potential disturbances. According to a Bayesia...

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a contro...