8,259 research outputs found
A new solution approach to polynomial LPV system analysis and synthesis
Based on sum-of-squares (SOS) decomposition, we propose a new solution approach for polynomial LPV system analysis and control synthesis problems. Instead of solving matrix variables over a positive definite cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
Stationary Cycling Induced by Switched Functional Electrical Stimulation Control
Functional electrical stimulation (FES) is used to activate the dysfunctional
lower limb muscles of individuals with neuromuscular disorders to produce
cycling as a means of exercise and rehabilitation. However, FES-cycling is
still metabolically inefficient and yields low power output at the cycle crank
compared to able-bodied cycling. Previous literature suggests that these
problems are symptomatic of poor muscle control and non-physiological muscle
fiber recruitment. The latter is a known problem with FES in general, and the
former motivates investigation of better control methods for FES-cycling.In
this paper, a stimulation pattern for quadriceps femoris-only FES-cycling is
derived based on the effectiveness of knee joint torque in producing forward
pedaling. In addition, a switched sliding-mode controller is designed for the
uncertain, nonlinear cycle-rider system with autonomous state-dependent
switching. The switched controller yields ultimately bounded tracking of a
desired trajectory in the presence of an unknown, time-varying, bounded
disturbance, provided a reverse dwell-time condition is satisfied by
appropriate choice of the control gains and a sufficient desired cadence.
Stability is derived through Lyapunov methods for switched systems, and
experimental results demonstrate the performance of the switched control system
under typical cycling conditions.Comment: 8 pages, 3 figures, submitted to ACC 201
On Incremental Stability of Interconnected Switched Systems
In this letter, the incremental stability of interconnected systems is
discussed. In particular, we consider an interconnection of switched nonlinear
systems. The incremental stability of the switched interconnected system is a
stronger property as compared to conventional stability. Guaranteeing such a
notion of stability for an overall interconnected nonlinear system is
challenging, even if individual subsystems are incrementally stable. Here,
preserving incremental stability for the interconnection is ensured with a set
of sufficient conditions. Contraction theory is used as a tool to achieve
incremental convergence. For the feedback interconnection, the small gain
characterisation is presented for the overall system's incremental stability.
The results are derived for a special case of feedback, i.e., cascade
interconnection. Matrix-measure-based conditions are presented, which are
computationally tractable. Two numerical examples are demonstrated and
supported with simulation results to verify the theoretical claims
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