##### Robust Control Design and Analysis
(Publications)

**Funding:** NASA, AFOSR

**Analysis of Convex Optimization Algorithms using IQCs:**
Large-scale optimization has become a central topic in big
data science. First-order black-box optimization methods have
been widely used in related machine learning problems, since
the oracle complexity of these methods can be independent of
the parameter dimension. In this project, we formulate
linear matrix inequality (LMI) conditions to analyze the
linear convergence rates of various deterministic and
stochastic optimization methods. All the resultant LMI
conditions are derived using integral quadratic constraints
(IQCs) and dissipation inequalities. This approach provides a
unified procedure to automate analysis for different
optimization methods.

**Graduate Student **: Bin Hu

(Publications)
**Robustness Analysis for Linear Parameter Varying
Systems:** This research focuses on developing tools and
methods for robustness analysis of linear parameter varying
(LPV) systems with respect to nonlinearities and/or
uncertainties. LPV systems are a class of linear systems where
the state matrices depend on (measurable) time-varying
parameters. The analysis assumes the input/output behavior of
the nonlinear/uncertain blocks is described by an integral
quadratic constraint (IQC). Dissipation inequality conditions
have been developed to bound the worst-case performance of the
uncertain LPV system. These tools can be used to analyze the
performance of gain-scheduled flight controllers. Future work
will consider the synthesis of robust controllers for
uncertain LPV systems.

**Postdoctoral Researcher**: Harald Pfifer

(Publications)
**Lower Bounds for the Gain of an LPV System:** Determining
the induced L2 norm of a linear, parameter-varying (LPV)
system is an integral part of the analysis and robust control
design procedures. In general, this norm cannot be determined
explicitly. Most prior work has focused on efficiently
computing upper bounds for the induced L2 gain. This work
focuses on developing complementary algorithms to compute
lower bounds for the induced L2 norm. The proposed lower bound
algorithm has two benefits. First, the lower bound complements
standard upper bound techniques. Specifically, a small gap
between the bounds indicates that further computation,
e.g. upper bounds with more complex Lyapunov functions, is
unnecessary. Second, the lower bound algorithm returns a "bad"
parameter trajectory for the LPV system that can be further
analyzed to provide insight into the system performance.

**Postdoctoral Researcher**: Tamas Peni

(Publications)