The problem of adaptive fuzzy control is investigated for a class of non-triangular structural stochastic switched nonlinear systems with full state constraints in this paper. A remarkable feature of the non-triangular structural nonlinear system is the so-called algebraic loop problem in existing backstepping-based analysis and design. Properties of fuzzy basis functions are utilized to circumvent the algebraic loop problem. Based on the Barrier Lyapunov function (BLF), an adaptive fuzzy stochastic switched control scheme is designed. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) with full state constraints. The effectiveness of the proposed control scheme is verified via simulation studies.

The paper develops a technique for solving a linear equation $Ax=b$ with a square and nonsingular matrix $A$, using a decentralized gradient algorithm. In the language of control theory, there are $n$ agents, each storing at time $t$ an $n$-vector, call it $x_i(t)$, and a graphical structure associating with each agent a vertex of a fixed, undirected and connected but otherwise arbitrary graph $\mathcal G$ with vertex set and edge set $\mathcal V$ and $\mathcal E$ respectively. We provide differential equation update laws for the $x_i$ with the property that each $x_i$ converges to the solution of the linear equation exponentially fast. The equation for $x_i$ includes additive terms weighting those $x_j$ for which vertices in $\mathcal G$ corresponding to the $i$-th and $j$-th agents are adjacent. The results are extended to the case where $A$ is not square but has full row rank, and bounds are given on the convergence rate.

Two asynchronous distributed algorithms are presented for solving a linear equation of the form Ax=b with at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming that each agent knows only a subset of the rows of the partitioned matrix [A\ \ b], the estimates of the equation's solution generated by its neighbors, and nothing more. Neighbor relationships are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relationships. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by its neighbors which are transmitted with delays. The event time sequences of different agents are not assumed to be synchronized. It is shown that for any matrix-vector pair (A, b) for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents' event times, the algorithms cause all agents' estimates to converge exponentially fast to the same solution to Ax=b. The first algorithm requires a specific initialization step at each agent, and the second algorithm works for arbitrary initializations. Explicit expressions for convergence rates are provided, and a relation between local initializations and limiting consensus solutions is established, which is used to solve the least 2-norm solution.

In the paper, an adaptive fault estimation approach is proposed for a class of switched nonlinear systems. The considered system is assumed to possess unknown nonlinearities, unmeasured states, and simultaneous sensor and actuator faults. Fuzzy logic systems are applied to approximate the unknown nonlinear terms. Two new adaptive fuzzy observers are designed where the sensor and actuator faults can be estimated separately. On the basis of average dwell time approach and Lyapunov stability theory, the resulting error system is proved to be bounded stable with designed parameters. Finally, a simulation example is provided to illustrate the effectiveness of the designed observers.

In this paper, we consider a dynamical system whose trajectory is a result of minimizing a multiphase cost function. The multiphase cost function is assumed to be a weighted sum of specified features (or basis functions) with phase-dependent weights that switch at some unknown phase transition points. A new inverse optimal control approach for recovering the cost weights of each phase and estimating the phase transition points is proposed. The key idea is to use a length-adapted window moving along the observed trajectory, where the window length is determined by finding the minimal observation length that suffices for a successful cost weight recovery. The effectiveness of the proposed method is first evaluated on a simulated robot arm, and then, demonstrated on a dataset of human participants performing a series of squatting tasks. The results demonstrate that the proposed method reliably retrieves the cost function of each phase and segments each phase of motion from the trajectory with a segmentation accuracy above 90%.