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We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk constraints. We propose a convex relaxation, and we present various theoretical properties. In particular, we show that the relaxation is exact under some assumptions. Also, we rewrite the relaxation as a Second Order Cone Programming (SOCP) problem. This has a relevant practical impact, since solvers for SOCP problems are quite efficient and allow solving large instances within tenths of a second. We performed many numerical tests, and in all of them the relaxation turned out to be exact. For this reason, we conjecture that the convex relaxation is always exact, although we could not give a formal proof of this fact.

We take a divide and conquer approach to design controllers for reachability problems given large-scale linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. We treat the couplings as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. The main contribution of this paper is a method to derive the contracts via a novel parameterization and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems. We present numerical examples, including a scalability study on a system with tens of thousands of dimensions, and a simple case study on applying our method to a distributed Model Predictive Control (MPC) problem in a power system.

This paper revisits a classical adaptive control problem: adaptive state tracking control of a state-space plant model, and solves the open discrete-time state tracking model reference adaptive control problem. Adaptive state tracking control schemes for continuous-time systems have been reported in the literature, using a Lyapunov-algorithm based design and analysis procedure. Such a procedure has not been successfully applied to the discrete-time adaptive state tracking control problem which has remained open. In this paper, new adaptive state tracking control schemes are developed for discrete-time systems, using gradient algorithms for updating the controller parameters. Both direct and indirect adaptive designs are derived, which have the desired parameter adaptation properties and closed-loop system stability and state tracking properties. Such a new gradient-algorithm based framework is also applicable to the continuous-time adaptive state tracking control problem to develop new solutions, as compared with the traditional Lyapunov-algorithm based solutions.

This paper proposes a robust formation control scheme for networked multi-tilt tricopter UAVs utilizing the Negative Imaginary (NI) and Positive Real (PR) theory. A Sliding Mode Control (SMC) scheme is designed for a multi-tilt tricopter to ensure stable hovering at a desired height. Then, a modified Subspace-based system identification algorithm is devised to identify a six-by-six NI model of the inner-loop-SMC-controlled tricopter in the continuous-time domain by exploiting the Laguerre filter. A two-loop formation control scheme has been developed for networked multi-tilt tricopters where the inner loop of each tricopter applies the SMC scheme, and the outer loop implements a distributed output feedback controller that satisfies the ‘mixed’ Strictly NI (SNI) + Strictly PR (SPR) system properties. Subsequently, we have established the robustness of the proposed scheme against NI/PR-type uncertainties and sudden loss of agents. The eigenvalue loci (also known as characteristic loci) technique is used instead of the Lyapunov-based approach to prove the asymptotic stability of the formation control scheme. An in-depth simulation case study was performed on a group of six inner-loop-SMC-controlled multi-tilt tricopters connected via a network to achieve a formation control mission, even in the presence of uncertainties.

We present a study of a class of closed Michaelis–Menten network models, which includes models of two categories of biochemical networks previously studied in the literature namely, processive and mixed mechanism phosphorylation futile cycle networks. The main focus of our study is on the uniqueness and stability of equilibrium points of this class of models. Firstly, we demonstrate that the total species concentration is a conserved quantity in models of this class. Next, we prove the existence of a unique positive equilibrium point in the set of points that correspond to a given total species concentration, using the intermediate value property of continuous functions. Finally, we demonstrate the asymptotic stability of this equilibrium point with respect to all initial conditions in the positive orthant that correspond to the same total species concentration as the equilibrium point, by constructing an appropriate Lyapunov function.

This paper addresses distributed state estimation in a peer-to-peer heterogeneous sensor network characterized by varying qualities of local estimators. The proposed approach employs weighted Kullback–Leibler average of local posteriors, considering both average consensus and distributed flooding protocols to efficiently disseminate information throughout the network. Our consensus and flooding methods extend communication and fusion to include designed local weighting factors. In addition, we present a unified framework for flooding, tailored to accommodate networks with arbitrarily limited communication bandwidth. By applying these methods to average local posteriors, we derive consensus-based and flooding-based distributed state estimators. Stability of the proposed estimators is analyzed for linear systems under network connectivity and system observability. Finally, simulation results demonstrate the effectiveness of the proposed approach.

The model reduction problem in the Loewner framework for port-Hamiltonian and network systems on graphs is studied. In particular, given a set of right-tangential interpolation data, the (subset of) left-tangential interpolation data that allow constructing an interpolant possessing a port-Hamiltonian structure is characterized. In addition, conditions under which an interpolant retains the underlying port-Hamiltonian structure of the system generating the data are given by requiring a particular structure of the generalized observability matrix. Ipso facto a characterization of the reduced order model in terms of Dirac structure with the aim of relating the Dirac structure of the underlying port-Hamiltonian system with the Dirac structure of the constructed interpolant is given. This result, in turn, is used to solve the model reduction problem in the Loewner framework for network systems described by a weighted graph. The problem is first solved, for a given clustering, by giving conditions on the right- and left-tangential interpolation data that yield an interpolant possessing a network structure. Thereafter, for given tangential data obtained by sampling an underlying network system, we give conditions under which we can select a clustering and construct a reduced model preserving the network structure. Finally, the results are illustrated by means of a second order diffusively coupled system and a first order network system.

This paper deals with cooperative output tracking problems for heterogeneous networks of linear agents. To refine high-precision tracking performances of agents, a graph-based distributed learning control (DLC) law is proposed, for which a new bounded-initialization, bounded-updating (BIBU) stability property is explored under any bounded initial conditions. Moreover, a class of heterogeneous-to-homogeneous transformation methods is introduced, together with presenting feasible gain design conditions, for DLC. It is shown that with the designed DLC law, not only can the effect of the agents’ heterogeneous dynamics in performing DLC be well overcome, but also the BIBU stability and the robust cooperative output tracking of agents can be simultaneously accomplished. A simulation test is also implemented to verify the validity of our developed DLC results for heterogeneous vehicle networks.

This paper is concerned with identifying the instantaneous modal parameters of forced oscillatory systems with response-dependent generalized inertia (mass, inductance, or equivalent) based on their measured dynamics. An identification method is proposed, which is a variation of the ”FORCEVIB” method. The method utilizes analytic signal representation and the properties of the Hilbert transform to obtain an analytic relationship between a system’s natural frequency and damping coefficient to its response and excitation signals. The proposed method is validated by comparing the identification results to the asymptotic solution of a simple system with response-dependent inertia and is then demonstrated, numerically and experimentally, for other more complicated nonlinear systems.

In this paper, exponential stability of discrete-time Markov jump linear systems (MJLSs) with the Markov chain on a Borel space $(\Theta ,B\left(\Theta \right))$ is studied, and bounded real lemmas (BRLs) are given. The work generalizes the results from the previous literature that considered only the Markov chain taking values in a countable set to the scenario of an uncountable set and provides unified approaches for describing exponential stability and $H_{\infty }$ performance of MJLSs. This paper covers two kinds of exponential stabilities: one is exponential mean-square stability with conditioning (EMSSy-C), and the other is exponential mean-square stability (EMSSy). First, based on the infinite-dimensional operator theory, the equivalent conditions for determining these two kinds of stabilities are shown respectively by the exponentially stable evolutions generated by the corresponding bounded linear operators on different Banach spaces, which turn out to present the spectral criteria of EMSSy-C and EMSSy. Furthermore, the relationship between these two kinds of stabilities is discussed. Moreover, some easier-to-check criteria are established for EMSSy-C of MJLSs in terms of the existence of uniformly positive definite solutions of Lyapunov-type equations or inequalities. In addition, BRLs are given separately in terms of the existence of solutions of the $\Theta$-coupled difference Riccati equation for the finite horizon case and algebraic Riccati equation for the infinite horizon case, which facilitates the $H_{\infty }$ analysis of MJLSs with the Markov chain on a Borel space.