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Determining the distance between a controllable system to the set of uncontrollable systems, namely, the controllability radius problem, has been extensively studied in the past. However, the opposite direction, that is, determining the `distance' between an uncontrollable system to the set of controllable systems, has seldom been considered. In this paper, we address this problem by defining the notion of zero-norm distance to controllability (ZNDC) to be the smallest number of entries (parameters) in the system matrices that need to be perturbed to make the original system controllable. We show genericity exists in this problem, so that other matrix norms (such as the $2$-norm or the Frobenius norm) adopted in this notion are nonsense. For ZNDC, we show it is NP-hard to compute, even when only the state matrix can be perturbed. We then provide some nontrivial lower and upper bounds. For its computation, we provide two heuristic algorithms. The first one is by transforming the ZNDC into a problem of structural controllability of linearly parameterized systems, and then greedily selecting the candidate links according to a suitable objective function. The second one is based on the weighted $l_1$-norm relaxation and the convex-concave procedure, which is tailored for ZNDC when additional structural constraints are involved in the perturbed parameters. Finally, we examine the performance of our proposed algorithms in several typical uncontrollable networks in multi-agent systems.

This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the inputs of the smallest possible cost with a bound on their cardinality, all to ensure system structural controllability. Those problems have attracted much attention recently; unfortunately, they are NP-hard in general. In this paper, it is found that, if the input structure satisfies certain `regularizations', which are characterized by the proposed restricted total unimodulairty notion, those problems can be solvable in polynomial time via linear programming (LP) relaxations. Particularly, the obtained characterizations depend only on the incidence matrix relating the inputs and the source strongly connected components (SCC) of the system structure, irrespective of how the inputs actuate states within the same SCC. They cover all the currently known polynomially solvable cases (such as the dedicated input case), and contain many new cases unexploited in the past, among which the source-SCC separated input (SSSI) constraint is highlighted. Further, for switched systems, the obtained polynomially solvable condition (namely the joint SSSI constraint) does not require each of the subsystems to satisfy the SSSI constraint. We achieve these by first formulating those problems as equivalent integer linear programmings (ILPs), and then proving total unimodularity of the corresponding constraint matrices. This property allows us to solve those ILPs efficiently via LP-relaxation. We also discuss solutions obtained via LP-relaxation and LP-rounding in the general case. Several examples are given to illustrate the obtained theoretical results., Comment: Extended version of an IEEE CDC 2022 paper

Nowadays, the rapid increases of the scale and complexity of the controlled plants bring new challenges such as computing power and storage for conventional control systems. Cloud computing is concerned as a powerful solution to handle the complex large-scale control missions using sufficient computing resources. However, the developed computing ability enables more complex devices and mass data being involved and thus the applications of model-based algorithms are constrained. Motivated by the above, we propose an original data-driven predictive cloud control system. To achieve the proposed system, a practical data-driven predictive cloud control platform rather than only a numerical simulator is established and together a cloud-edge communication scheme is developed. Finally, the verification of simulations and experiments as well as discussions demonstrate the effectiveness of the proposed system.

The discrepancy between theory and experiment severely limits the development of quantum key distribution (QKD). Reference-frame-independent (RFI) protocol has been proposed to avoid alignment of the reference frame. However, multiple optical modes caused by Trojan horse attacks and equipment loopholes lead to the imperfect emitted signal unavoidably. In this paper, we analyzed the security of the RFI-QKD protocol with non-qubit sources based on generalizing loss-tolerant techniques. The simulation results show that our work can effectively defend against non-qubit sources including a misaligned reference frame, state preparation flaws, multiple optical modes, and Trojan horse attacks. Moreover, it only requires the preparation of four quantum states, which reduces the complexity of the experiment in the future., Comment: 8 pages, 1 figure

In this paper, we investigate the fixed-time behavioral control problem for a team of second-order nonlinear agents, aiming to achieve a desired formation with collision/obstacle~avoidance. In the proposed approach, the two behaviors(tasks) for each agent are prioritized and integrated via the framework of the null-space-based behavioral projection, leading to a desired merged velocity that guarantees the fixed-time convergence of task errors. To track this desired velocity, we design a fixed-time sliding mode controller for each agent with state-independent adaptive gains, which provides a fixed-time convergence of the tracking error. The control scheme is implemented in a distributed manner, where each agent only acquires information from its neighbors in the network. Moreover, we adopt an online learning algorithm to improve the robustness of the closed system with respect to uncertainties/disturbances. Finally, simulation results are provided to show the effectiveness of the proposed approach.

In this paper, two robust model predictive control (MPC) schemes are proposed for tracking control of nonholonomic systems with bounded disturbances: tube-MPC and nominal robust MPC (NRMPC). In tube-MPC, the control signal consists of a control action and a nonlinear feedback law based on the deviation of the actual states from the states of a nominal system. It renders the actual trajectory within a tube centered along the optimal trajectory of the nominal system. Recursive feasibility and input-to-state stability are established and the constraints are ensured by tightening the input domain and the terminal region. While in NRMPC, an optimal control sequence is obtained by solving an optimization problem based on the current state, and the first portion of this sequence is applied to the real system in an open-loop manner during each sampling period. The state of nominal system model is updated by the actual state at each step, which provides additional a feedback. By introducing a robust state constraint and tightening the terminal region, recursive feasibility and input-to-state stability are guaranteed. Simulation results demonstrate the effectiveness of both strategies proposed.