A systematic controller design procedure is developed for the class of linear time-invariant systems which use both continuous and bang-bang control effectors. The sampled-data regulator and its associated weighting matrices and cost function are extended to this class of system, and are used to modulate the bang-bang effector to achieve desired performance levels. Stability, sensitivity, and r...

This study explores the effectiveness of applying optimal control techniques to the flight control law clearance problem, which is the challenge of ensuring the safety of an aircraft’s flight control system for all allowable inputs. The main criteria chosen were the angle-ofattack limit exceeding criterion in the longitudinal plane, and the angle-of-sideslip limit exceeding criterion in the lat...

The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging problem in optimal control theory for which closed-form solutions exist only for a few systems of small dimensions. This paper presents a very generic solution...

This paper addresses the problem of designing jerk limited timeoptimal control profiles for rest-to-rest maneuvers of flexible structures. The variation of the structure of the jerk profile as a function of the permissible jerk is studied. An optimal control problem is formulated which includes constraints to cancel the poles corresponding to the rigid body and flexible modes of the system and ...

We consider an expression for the second–order variation (SOV) of bang-bang controls derived by Agrachev and Gamkrelidze. The SOV plays an important role in both necessary and sufficient second–order optimality conditions for bang-bang controls. These conditions are stronger than the one provided by the first–order Pontryagin maximum principle (PMP). For a bang-bang control with k switching poi...

In this preliminary work we give a geometric characterization of the time-optimal trajectories for piecewise affine bistable switch. Such hybrid models play major role in systems biology, as they can expressively account behaviors simple gene-regulatory networks. A key example these biological circuits is genetic toggle switch, which optimality state switch has not been studied to present day. ...

We develop a continuous-time control approach to optimal trading in Proof-of-Stake (PoS) blockchain, formulated as consumption-investment problem that aims strike the balance between participant's (or agent's) utility from holding/trading stakes and consumption. present solutions via dynamic programming Hamilton-Jacobi-Bellman (HJB) equations. When functions are linear or convex, we derive clos...

Let (Bt )0≤t≤T be either a Bernoulli random walk or a Brownian motion with drift, and let Mt := max{Bs : 0 ≤ s ≤ t}, 0 ≤ t ≤ T . In this paper we solve the general optimal prediction problem sup0≤τ≤T E[f (MT −Bτ )], where the supremum is over all stopping times τ adapted to the natural filtration of (Bt ) and f is a nonincreasing convex function. The optimal stopping time τ∗ is shown to be of ‘...

We present a novel static power control scheme to improve system capacity in wireless cellular networks. Our basic idea is to reduce intercellular interference and improve the capture probability by coordinating transmission powers of users in different cells. This coordination is determined beforehand and no real-time coordination is required. Power control is static and fixed. We formulate an...