Leila Jasmine Bridgeman

Conic-sector-based control to circumvent passivity violations

This paper explores the use of the Conic Sector Theorem for both stability analysis and controller design. Ensuring input-output stability of plants experiencing passivity violations is the motivation behind this work. Given a previously designed controller and plant that has experienced a (partially unknown) passivity violation, a novel sector bound selection procedure is presented. This procedure can be used to assess input-output stability of the violated plant and original controller via the Conic Sector Theorem. Should input-output stability not be ensured, two original controller synthesis methods are suggested: one is designed to mimic the H2 controller, and the other is inspired by strictly positive real controller synthesis. Both methods guarantee input-output stability by selecting controllers within appropriate conic sectors, and involve only the evaluation of readily solvable linear matrix inequalities and algebraic Riccati inequalities. A numerical simulation is provided as a proof of concept.

Conic-sector-based controller synthesis: Theory and experiments

The Passivity Theorem is a popular input-output stability analysis tool. However, passivity violations, which are often due to sensor and actuator dynamics, may cause instabilities, necessitating the adoption of alternative stability results. This paper presents experimental results employing controllers that ensure stability via the Conic Sector Theorem. A new conic sector controller synthesis method mimicking an ℋ2-optimal controller is presented and compared to an existing conic sector controller synthesis method, and an ℋ2 controller itself. The conic controllers are found to yield increased robustness and improved performance in the presence of passivity violations.

Stability and feasibility of MPC for switched linear systems with dwell-time constraints

This paper considers the control of discrete-time switched linear systems using model predictive control. A model predictive controller is designed with terminal cost and constraints depending on the terminal mode of the switched linear system. Conditions on the terminal cost and constraints are presented to ensure persistent feasibility and stability of the closed-loop system given sufficiently long dwell-time. A procedure is proposed to numerically compute admissible terminal costs and constraint sets.

The exterior conic sector lemma

The conic sector theorem is a powerful input–output stability analysis tool, providing a fine balance between generality and simplicity of system characterisations that is conducive to practical stability analysis and robust controller synthesis. Without means to systematically identify and impose exterior conic properties, existing analysis and synthesis methods are limited to employing a special case of the conic sector theorem which may prove overly conservative when considering very strictly passive plants. This paper removes the current limitation by establishing the exterior conic sector lemma, which provides matrix inequalities equivalent to exterior conic bounds for linear time-invariant systems.

Conic-Sector-based control to circumvent passivity violations

This paper explores the use of the Conic Sector Theorem for both stability analysis and controller design. Ensuring input-output stability of plants experiencing passivity violations is the motivation behind this work. Given a previously designed controller and plant that has experienced a (partially unknown) passivity violation, a novel sector bound selection procedure is presented. This procedure can be used to assess input-output stability of the violated plant and original controller via the Conic Sector Theorem. Should input-output stability not be ensured, two original controller synthesis methods are suggested: one is designed to mimic the H2 controller, and the other is inspired by strictly positive real controller synthesis. Both methods guarantee input-output stability by selecting controllers within appropriate conic sectors, and involve only the evaluation of readily solvable linear matrix inequalities and algebraic Riccati inequalities. A numerical simulation is provided as a proof of concept.

The Extended Conic Sector Theorem

Input-output stability theory is an indispensable tool in control engineering. However, classic results such as the Conic Sector Theorem, cannot be applied in some important cases. This technical note extends the original Conic Sector Theorem to apply to open-loop unstable systems and those with negative upper conic bounds and incorporates a careful treatment of degenerate conic systems and alterations accounting for nonzero initial conditions. Simulations highlight how the contributions facilitate robust control in the most challenging of circumstances.

A Comparative Study of Input–Output Stability Results

At present, many similar but disparate input–output (I–O) stability criteria exist. Without means for comparison, it is unclear which result is best used in any given application. This paper proposes a means for comparison between I–O stability results involving norms and inner products of inputs and outputs. The extended conic sector theorem provides a framework for determining which results are least conservative and most broadly applicable. In so-doing, numerous existing stability results are unified and revealed as more powerful than previously thought.

Constraint satisfaction for switched linear systems with restricted dwell-time

This paper considers the control of constrained linear systems with dynamics and constraints that change as a function of time according to an unknown exogenous switching signal that satisfies dwell-time restrictions. We characterize the set of initial conditions for which it is possible to guarantee constraint satisfaction for any admissible switching signal. We define the concept of control (positive) switch-invariant sets which are control (positive) invariant sets with the additional property that it is possible to transition between the control (positive) switch-invariant sets without violating constraints. It is possible to guarantee constraint satisfaction for a given initial condition if the control (positive) switch-invariant set of a mode can be reached from it within the dwell-time of that mode. An algorithm is presented for computing the maximal control (positive) switch-invariant sets. Finally, we demonstrate the theory developed in this paper on a vehicle lane changing case study.

Conic controller synthesis that minimizes an upper bound on the closed-loop ℋ 2 -norm

The Conic Sector Theorem is a versatile input-output stability result that can be used to ensure closed-loop, input-output stability where better-known results, such as the Passivity and Small Gain Theorems, cannot. Moreover, conic sectors can be used to characterize a variety of input-output properties, such as gain, phase, and minimum gain. This paper proposes a linear-matrix-inequality-based approach to the synthesis of conic controllers that minimize an upper-bound on the closed-loop v-norm. This provides a valuable tool for robust and optimal control by combining the utility of conic sectors and the Conic Sector Theorem with ℋ2-optimal control.

Norm- and linear-inequality-constrained state estimation: An LMI approach

This paper proposes a method for state estimation that incorporates norm- and linear-inequality constraints using Linear Matrix Inequalities (LMIs). This is accomplished by adopting a prediction-correction filter form and calculating the observer gain matrix by solving a convex optimization problem with LMI constraints where the state constraints are expressed as LMIs. The state constraints considered in this study include norm and linear inequalities. Simulation results are included to assess the performance of the proposed filter in a scenario involving a mobile robot moving within a constrained area taking range and bearing measurements of known landmarks. The filters performance is compared with a traditional EKF.