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Finite-Time Attitude Synchronization with Distributed Discontinuous Protocols ; ; et al in IEEE Transactions on Automatic Control (in press) The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed ... [more ▼] The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper. [less ▲] Detailed reference viewed: 61 (1 UL)Network Identifiability from Intrinsic Noise Goncalves, Jorge ; ; in IEEE Transactions on Automatic Control (in press) Detailed reference viewed: 318 (25 UL)Almost Global Consensus on the n-Sphere Markdahl, Johan ; Thunberg, Johan ; Goncalves, Jorge in IEEE Transactions on Automatic Control (2018), 63(6), 1664-1675 This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multi-agent systems that evolve in continuous time on the n-dimensional unit ... [more ▼] This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multi-agent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all n 2 N\{1}, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the n-sphere for n 2 N\{1} differs from the circle and SO(3) where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on SO(3) by combining two almost globally convergent protocols on the n-sphere for n in {1, 2}. Theoretical and simulation results suggest that the combined protocol yields almost global consensus on SO(3). [less ▲] Detailed reference viewed: 77 (5 UL)Local Lyapunov Functions for Consensus in Switching Nonlinear Systems Thunberg, Johan ; Goncalves, Jorge ; in IEEE Transactions on Automatic Control (2017) This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in Rm and have switching interconnection topologies. Both the first ... [more ▼] This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in Rm and have switching interconnection topologies. Both the first theorem, formulated in terms of the states of individual agents, and the second theorem, formulated in terms of the pairwise states for pairs of agents, can be interpreted as variants of Lyapunov’s second method. The two theorems complement each other; the second provides stronger convergence results under weaker graph topology assumptions, whereas the first often can be applied in a wider context in terms of the structure of the right-hand sides of the systems. The second theorem also sheds some new light on well-known results for consensus of nonlinear systems where the right-hand sides of the agents’ dynamics are convex combinations of directions to neighboring agents. For such systems, instead of proving consensus by using the theory of contracting convex sets, a local quadratic Lyapunov function can be used. [less ▲] Detailed reference viewed: 134 (4 UL)Global State Synchronization in Networks of Cyclic Feedback Systems ; ; et al in IEEE Transactions on Automatic Control (2012), 57(2), 478-483 This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback ... [more ▼] This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. [less ▲] Detailed reference viewed: 67 (0 UL)A Linear Programming Approach to Parameter Fitting for the Master Equation ; Goncalves, Jorge in IEEE Transactions on Automatic Control (2009), 54(10), 2451-2455 This technical note proposes a new framework for the design of continuous time, finite state space Markov processes. In particular, we propose a paradigm for selecting an optimal matrix within a pre ... [more ▼] This technical note proposes a new framework for the design of continuous time, finite state space Markov processes. In particular, we propose a paradigm for selecting an optimal matrix within a pre-specified pencil of transition rate matrices. Given any transition rate matrix specifying the time-evolution of the Markov process, we propose a class of figures of merit that upper-bounds the long-term evolution of any statistical moment. We show that optimization with respect to the aforementioned class of cost functions is tractable via dualization and linear programming methods. In addition, we suggest how this approach can be used as a tool for the sub-optimal design of the master equation, with performance guarantees. Our results are applied to illustrative examples. [less ▲] Detailed reference viewed: 68 (1 UL)Necessary and sufficient conditions for dynamical structure reconstruction of LTI networks Goncalves, Jorge ; in IEEE Transactions on Automatic Control (2008), 53(7), 1670-1674 This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable ... [more ▼] This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input–output data, not even Boolean reconstruction is possible, in general, without more information about the system.We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality. [less ▲] Detailed reference viewed: 62 (1 UL)Regions of stability for limit cycle oscillations in piecewise linear systems Goncalves, Jorge in IEEE Transactions on Automatic Control (2005), 50(11), 1877-1882 Oscillations appear in numerous applications from biology to technology.However, besides local results, rigorous stability and robustness analysis of oscillations are rarely done due to their intrinsic ... [more ▼] Oscillations appear in numerous applications from biology to technology.However, besides local results, rigorous stability and robustness analysis of oscillations are rarely done due to their intrinsic nonlinear behavior. Poincarémaps associated with the system cannot typically be found explicitly and stability is estimated using extensive simulations and experiments. This paper gives conditions in the form of linear matrix inequalities (LMIs) that guarantee asymptotic stability in a reasonably large region around a limit cycle for a class of systems known as piecewise linear systems (PLS). Such conditions, based on recent results on impact maps and surface Lyapunov functions (SuLF), allow a systematic and efficient analysis of oscillations of PLS or arbitrarily close approximations of nonlinear systems by PLS. The methodology applies to any locally stable limit cycle of a PLS, regardless of the dimension and the number of switching surfaces of the system, and is illustrated with a biological application: a fourth-order neural oscillator, also used in many robotics applications such as juggling and locomotion. [less ▲] Detailed reference viewed: 89 (0 UL)Global analysis of piecewise linear systems using impact maps and quadratic surface Lyapunov functions Goncalves, Jorge ; ; in IEEE Transactions on Automatic Control (2003), 48(12), 2089-2106 This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely ... [more ▼] This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be “unfriendly” maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS. [less ▲] Detailed reference viewed: 118 (1 UL)L2-gain of double integrators with saturation nonlinearity Goncalves, Jorge in IEEE Transactions on Automatic Control (2002), 47(12), 2063-2068 This note uses quadratic surface Lyapunov functions (SuLFs) to efficiently check if a double integrator in feedback with a saturation nonlinearity has L -gain less than > 0. We show that for many such ... [more ▼] This note uses quadratic surface Lyapunov functions (SuLFs) to efficiently check if a double integrator in feedback with a saturation nonlinearity has L -gain less than > 0. We show that for many such systems, the L -gain is nonconservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of 1. These results allow the use of classical analysis tools like -analysis or integral quadratic constraints to analyze systems with double integrators and saturations, including servo systems like some mechanical systems, satellites, hard disks, compact disk players, etc. [less ▲] Detailed reference viewed: 80 (0 UL)Global stability of relay feedback systems Goncalves, Jorge ; ; in IEEE Transactions on Automatic Control (2001), 46(4), 550--562 For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global ... [more ▼] For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global stability conditions, however, are practically nonexistent. This paper presents conditions in the form of linear matrix inequalities (LMIs) that, when satisfied, guarantee global asymptotic stability of limit cycles induced by relays with hysteresis in feedback with linear time-invariant (LTI) stable systems. The analysis consists in finding quadratic surface Lyapunov functions for Poincaré maps associated with RFS. These results are based on the discovery that a typical Poincaré map induced by an LTI flow between two hyperplanes can be represented as a linear transformation analytically parametrized by a scalar function of the state. Moreover, level sets of this function are convex subsets of linear manifolds. The search for quadratic Lyapunov functions on switching surfaces is done by solving a set of LMIs. Although this analysis methodology yields only a sufficient criterion of stability, it has proved very successful in globally analyzing a large number of examples with a unique locally stable symmetric unimodal limit cycle. In fact, it is still an open problem whether there exists an example with a globally stable symmetric unimodal limit cycle that could not be successfully analyzed with this new methodology. Examples analyzed include minimum-phase systems, systems of relative degree larger than one, and of high dimension. Such results lead us to believe that globally stable limit cycles of RFS frequently have quadratic surface Lyapunov functions. [less ▲] Detailed reference viewed: 77 (0 UL) |
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