Chanying Li

State Observability and Observers of Linear-Time-Invariant Systems Under Irregular Sampling and Sensor Limitations

State observability and observer designs are investigated for linear-time-invariant systems in continuous time when the outputs are measured only at a set of irregular sampling time sequences. The problem is primarily motivated by systems with limited sensor information in which sensor switching generates irregular sampling sequences. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. It demonstrates that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual time sequences. This result extends Shannons sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarized.

Realizations of a Special Class of Admittances With Strictly Lower Complexity Than Canonical Forms

This paper investigates the simplified realization problem of a special class of positive-real admittances similar to biquadratic functions but with an extra pole at the origin, which is widely used in the analysis of suspension systems. The results in this paper are motivated by passive mechanical control with the inerter. The concept of strictly lower complexity is first defined, whose indices in this paper are the total number of elements, the number of resistors (dampers), and the number of capacitors (inerters). We then derive a necessary and sufficient condition for this class of admittance to be realized by the networks that are of strictly lower complexity than the canonical realization by the Foster Preamble method. To solve this problem, it is shown that it suffices to consider the following: 1) networks with at most four elements, 2) irreducible five-element resistor-inductor (RL) networks, and 3) irreducible five-element resisitor-inductor-capacitor (RLC) networks. Other cases are shown to be impossible. By finding their corresponding network configurations through a series of constraints and deriving the corresponding realizability conditions, the final condition can be obtained. Finally, the U-V plane and numerical examples are provided to illustrate the theoretical results.

Performance Benefits of Using Inerter in Semiactive Suspensions

This brief investigates the performance benefits of using inerter in semiactive suspensions. A novel structure for semiactive suspensions with inerter, which consists of a passive part and a semiactive part, is proposed. Six semiactive suspension struts, each of which employs an inerter in the passive part and a semiactive damper in the semiactive part, are introduced. Two suboptimal control laws named clipped optimal control and steepest gradient control laws are derived to control the damping coefficient in the semiactive part. Extensive simulations with respect to different choices of weighting factors and suspension static stiffnesses are conducted based on both a quarter car model and a full car model. The results show that, compared with the conventional semiactive suspension strut, the overall suspension performance can be significantly improved using inerters, including ride comfort, suspension deflection, and road holding. Comparative studies between these two suboptimal control laws and between these semiactive struts are also carried out to facilitate future practical application of the proposed semiactive suspensions with inerter.

On Exponential Almost Sure Stability of Random Jump Systems

This paper is concerned with a class of random jump systems represented by transition operators, which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case. A series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios. The stability criteria obtained are further extended to Markov jump linear systems with infinite states, and hence a unified approach to describing the almost sure stability of MJLSs is addressed under this context. All the results in the work are developed for both the continuous- and discrete-time systems.

On robust stability of discrete-time adaptive nonlinear control ☆

Abstract We consider adaptive control of discrete-time nonlinear systems with a single unknown parameter in this paper. We demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4. This result further confirms the conclusion of Guo [On critical stability of discrete-time adaptive nonlinear control, IEEE Trans. Automat. Control 42 (1997) 1488–1499] which addresses unbounded noise in a stochastic setting. Also in our worst-case approach, we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4.

Observer-Based Consensus Tracking of Nonlinear Agents in Hybrid Varying Directed Topology

The problem of leader-following consensus of nonlinear agents in hybrid varying directed topology is considering not only the agent but also that the directed edges can have a time-varying nonlinear dynamics with jump discontinuity, which contains the switching topology as its special case. This paper has the following contributions toward this problem. The leader-following consensus problem in hybrid varying directed topology is first addressed, and an online leader switching method is proposed, which reduces the dependence on some global conditions and the connectivity assumptions on the selection of leaders. Second, we generalize the Lipschitz condition and the combined condition of one-sided Lipschitz and quadratically inner-boundedness conditions to a new generalized linear incremental condition, which gives us a more generalized result in the Lyapunov proof and better performance in simulation. Third, an observer-based consensus protocol is constructed with two sufficient observability and controllability conditions and two optimal control design algorithms. Finally, an example of teleoperating multirobotic manipulator joint network is provided to illustrate the performance improvement by comparing with the existing results.

Synthesis of n-port resistive networks containing 2n terminals

This paper is concerned with the realizability problem of n-port resistive networks that contain 2n terminals. A necessary and sufficient condition for any real symmetric matrix to be realizable as the admittance of an n-port resistive network containing 2n terminals is obtained. This condition is based on the existence of a parameter matrix. Furthermore, the values of the elements are expressed in terms of the entries of the admittance matrix and the parameter matrix. Finally, a numerical example is used to illustrate the results. Copyright

Semi-active suspension with semi-active inerter and semi-active damper

Abstract This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by on-line control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed, where the target active control force derived by LQR control in the “Reciprocal State-Space” (RSS) framework is tracked by controlling the semi-active damping coefficient and semi-active inertance. One of the advantages of the proposed method is that it is straightforward to use the acceleration information in the controller design. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.

Consensus networks with switching topology and time-delays over finite fields

The consensus problem in networks with both switching topology and time-delays over finite fields is investigated in this paper. The finite field, which is a kind of finite alphabet, is considered due to the fact that networks often possess limited computation, memory, and capabilities of communication. First, by graph-theoretic method, one necessary and sufficient condition is derived for finite-field consensus of switching networks without time-delays. Subsequently, another necessary and sufficient condition on finite-field consensus without time-delays is provided based on FFC property of matrices associated with switching networks. Moreover, by means of the results on delay-free networks, some necessary and sufficient conditions for finite-field consensus of networks with both switching topology and time-delays are obtained. Additionally, it can be shown that switching networks with time-delays present in each self-transmission cannot achieve consensus.

STABILIZATION OF DISCRETE-TIME NONLINEAR UNCERTAIN SYSTEMS BY FEEDBACK BASED ON LS ALGORITHM ∗

This paper is concerned with the use of the least squares (LS) algorithm to design a feedback control law to stabilize a basic class of discrete-time nonlinear uncertain systems. The result shows that if a certain polynomial criterion is satisfied, the system can be stabilized by feedback based on the LS algorithm for Gaussian distributed noise and unknown parameters. This result thus provides an answer to the question of what are the fundamental limitations of the discrete-time adaptive nonlinear control. This issue of feedback capability has been an open problem for more than ten years since it was put forward.