15 problems

Consider the closed-loop system … Let $x_2$ converge to a constant and let $\omega(t,x_2)$ denote the periodic steady-state value approached by $u(t,x)$. Assume that…

Let $V^{\mathrm{f}}$ be the terminal cost and let $\lambda_{rs}$ denote the rotated stage-cost function associated with the receding horizon control problem. The notation…

Let a feedback system consist of an LTI system and a static, square-preserving nonlinearity, and suppose its oscillations are approximated using the square wave approximation of th…

Extremum seeking control involves an unknown plant model and objective function, and its high-frequency gain may change sign repeatedly near the optimum. A monitoring-function sche…

Let ISCD-MPC denote the iterative state- and control-dependent model predictive control technique described in the paper. A chain of integrators is a system formed by integrators o…

Periodic perturbation signals are used to probe an objective function, and an averaged objective function is the objective obtained by averaging the effect of those signals over th…

Consider the closed-loop Lurie system … where $x\in\mathbb R^n$ is the state, $A$, $B$, and $C$ are constant matrices, and $\Phi$ is a time-varying nonlinear feedback function belo…

Let horizon-dependent bounds $(\gamma_k)$ be used in the linear program defining the suboptimality factor $\alpha_N$, and let $\hat{\alpha}_N$ denote the analytical bound introduce…

Let $N$ be the prediction horizon, let $N_{\overline{Y}}$ denote the horizon appearing in the stability guarantees, and let $\alpha_N$ be the suboptimality index. The setting may i…

Let overset{raisebox{0ex}{scalebox{0.45}{\bullet}}}{x} =f(x,u) be the control system under consideration. Brockett's condition means that the vector field $f$ is open at the o…

Consider a control system overset{raisebox{0ex}{scalebox{0.45}{\bullet}}}{x} =f(x,u) and local asymptotic stabilizability by continuous feedback laws, without assuming uniquen…

Funnel-MPC feasibility conjecture. Feasibility of this Funnel-MPC scheme can be proved by using optimality of the predicted open-loop trajectories; in particular, feasibility along…

Existing nonlinear output-regulation frameworks often assume that the steady-state solutions depend on the exogenous signal through mappings $(x^\star,u^\star)=(\pi(w),c(w))$, and…

Let $E_r$ denote the right-invariant estimation error of the passive local partial state observer (LPSO), and suppose Assumption holds. Passive LPSO convergence conjecture. The pas…

For the nonlinear control system and time-varying MPC scheme considered above, let $m^\star$ denote the control horizon selected by the stability criterion in Theorem. In the class…